Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations
By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path depen...
Saved in:
| Published in | Potential analysis Vol. 61; no. 2; pp. 379 - 407 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.08.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0926-2601 1572-929X |
| DOI | 10.1007/s11118-023-10113-5 |
Cover
| Abstract | By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa-Holm equation with or without Coriolis effect has a unique global solution when the noise is strong enough, whereas for the deterministic model wave-breaking may occur. This indicates that the noise may prevent blow-up almost surely. |
|---|---|
| AbstractList | By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole history and the distribution under strong enough noise. As applications, the global existence and uniqueness are proved for distribution-path dependent stochastic transport type equations, which are arising from stochastic fluid mechanics with forces depending on the history and the environment. In particular, the distribution-path dependent stochastic Camassa-Holm equation with or without Coriolis effect has a unique global solution when the noise is strong enough, whereas for the deterministic model wave-breaking may occur. This indicates that the noise may prevent blow-up almost surely. |
| Author | Ren, Panpan Wang, Feng-Yu Tang, Hao |
| Author_xml | – sequence: 1 givenname: Panpan surname: Ren fullname: Ren, Panpan organization: Department of Mathematics, City University University of Hong Kong – sequence: 2 givenname: Hao orcidid: 0000-0003-3414-7345 surname: Tang fullname: Tang, Hao email: haot@math.uio.no organization: Department of Mathematics, University of Oslo – sequence: 3 givenname: Feng-Yu surname: Wang fullname: Wang, Feng-Yu organization: Center for Applied Mathematics, Tianjin University |
| BookMark | eNp9kEFPnCEQhomxiavtH_BE0jM6gPDB0bhrNTFq4jbpjVA-qJgtfAKbxn8vu6tp4sG5zGGe952Z9xDtp5w8QscUTijAcFppL0WAcUKBUk7EHppRMTCimf61j2agmSRMAj1Ah7U-AQAbBjVDbh5rK_H3usWcyL1tj3juJ59Gnxq-zWkVk7cFP9zPFxX_i318Pk2r6OyGxy3jh5bdo60tOrwsNtUpl4aXL5PHi-f1lqpf0ZdgV9V_e-tH6OflYnlxRW7uflxfnN8Qx5VqhHrOmFZi0yF46UehldNCnDnFVFBno9YSpHAUZNA-DDJQGGVwcrTBesaPEN75utKfismkXKyhoAQzlA5SiI583yFTyc9rX5t5yuuS-lWGg5LAgVHeKfVulGstPhgX2_aXVmxcdUuzSd3sUjc9dbNN3WwWsA_SqcS_trx8LuI7Ue1w-uPL_6s-Ub0CXMqVnA |
| CitedBy_id | crossref_primary_10_3934_dcdss_2024185 crossref_primary_10_1016_j_jmaa_2024_128912 crossref_primary_10_1016_j_cnsns_2024_108535 |
| Cites_doi | 10.1016/j.spa.2011.03.004 10.1103/PhysRevLett.71.1661 10.1214/21-AIHP1241 10.3934/dcds.2019125 10.1137/16M1080537 10.1214/12-AOP773 10.1016/j.spa.2014.01.010 10.1016/j.spa.2018.12.012 10.1007/s00440-004-0392-5 10.1016/j.jde.2019.05.016 10.1090/S0894-0347-1991-1086966-0 10.1007/s40072-023-00291-z 10.1007/s00205-008-0128-2 10.1016/j.jde.2021.02.019 10.1016/S0375-9601(03)00114-2 10.1016/j.spa.2021.01.008 10.1007/s10231-019-00882-5 10.1142/S0219199722500730 10.1016/j.jfa.2013.01.003 10.1007/BF02392586 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO;2-5 10.3934/dcds.2022163 10.1016/j.spa.2022.11.010 10.1007/s00222-009-0224-4 10.1007/s00030-015-0321-6 10.1007/978-3-0348-7909-5 10.1016/j.spa.2017.05.006 10.4310/CMS.2021.v19.n3.a2 10.1103/PhysRevLett.87.194501 10.1007/s00028-023-00890-2 10.2422/2036-2145.201512_008 10.1016/j.jmaa.2021.125000 10.1017/CBO9781139137119 10.1007/978-3-642-36297-2_2 10.1515/9783110492552 10.1017/CBO9781107295513 10.1214/ECP.v19-2833 10.1007/s00021-019-0432-7 10.1007/s00332-021-09755-9 10.1007/s00030-019-0602-6 10.1007/s10231-017-0633-8 10.1007/978-3-642-18231-0 10.1016/j.jfa.2023.110075 10.1016/0167-2789(81)90004-X |
| ContentType | Journal Article |
| Copyright | The Author(s) 2024 The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. info:eu-repo/semantics/openAccess |
| Copyright_xml | – notice: The Author(s) 2024 – notice: The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. – notice: info:eu-repo/semantics/openAccess |
| DBID | C6C AAYXX CITATION 3HK |
| DOI | 10.1007/s11118-023-10113-5 |
| DatabaseName | Springer Nature OA Free Journals CrossRef NORA - Norwegian Open Research Archives |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: C6C name: Springer Nature OA Free Journals url: http://www.springeropen.com/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Mathematics |
| EISSN | 1572-929X |
| EndPage | 407 |
| ExternalDocumentID | 10852_117655 10_1007_s11118_023_10113_5 |
| GrantInformation_xml | – fundername: National Key Research & Development Program of China grantid: No.2020YFA0712900 and No. 2022YFA1006000 – fundername: Alexander von Humboldt-Stiftung funderid: http://dx.doi.org/10.13039/100005156 – fundername: National Natural Science Foundation of China grantid: 11831014; 11921001 funderid: http://dx.doi.org/10.13039/501100001809 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C .86 .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 29O 2J2 2JN 2JY 2KG 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 8TC 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFDYV AFEXP AFGCZ AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA BSONS C6C CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS H13 HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9R PF0 PT4 PT5 QOK QOS R4E R89 R9I RHV RNI ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 ZMTXR ZWQNP ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP ATHPR AYFIA CITATION ABRTQ 3HK |
| ID | FETCH-LOGICAL-c388t-1e3229851e320fe6ed598c9554c828f84d996065c106f9ef76f10d6fc6dafae23 |
| IEDL.DBID | C6C |
| ISSN | 0926-2601 |
| IngestDate | Mon Mar 31 03:23:22 EDT 2025 Thu Sep 25 00:42:59 EDT 2025 Tue Jul 01 01:52:26 EDT 2025 Thu Apr 24 23:00:07 EDT 2025 Fri Feb 21 02:39:56 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | Distribution-Path Dependent Nonlinear SPDEs 35Q35 35A01 Secondary: 60H30 Stochastic transport type equation Stochastic Camassa-Holm type equation Primary: 60H15 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c388t-1e3229851e320fe6ed598c9554c828f84d996065c106f9ef76f10d6fc6dafae23 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ORCID | 0000-0003-3414-7345 |
| OpenAccessLink | https://doi.org/10.1007/s11118-023-10113-5 |
| PQID | 3086030213 |
| PQPubID | 2043741 |
| PageCount | 29 |
| ParticipantIDs | cristin_nora_10852_117655 proquest_journals_3086030213 crossref_citationtrail_10_1007_s11118_023_10113_5 crossref_primary_10_1007_s11118_023_10113_5 springer_journals_10_1007_s11118_023_10113_5 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2024-08-01 |
| PublicationDateYYYYMMDD | 2024-08-01 |
| PublicationDate_xml | – month: 08 year: 2024 text: 2024-08-01 day: 01 |
| PublicationDecade | 2020 |
| PublicationPlace | Dordrecht |
| PublicationPlace_xml | – name: Dordrecht |
| PublicationSubtitle | An International Journal Devoted to the Interactions between Potential Theory, Probability Theory, Geometry and Functional Analysis |
| PublicationTitle | Potential analysis |
| PublicationTitleAbbrev | Potential Anal |
| PublicationYear | 2024 |
| Publisher | Springer Netherlands Springer Nature B.V |
| Publisher_xml | – name: Springer Netherlands – name: Springer Nature B.V |
| References | Pardoux (CR22) 1972; 275 Constantin, Escher (CR39) 1998; 51 Tang, Yang (CR45) 2023; 59 Holden, Karlsen, Pang (CR44) 2023; 43 CR37 Dullin, Gottwald, Holm (CR36) 2001; 87 CR32 CR30 Chen, Duan, Gao (CR42) 2021; 19 Flandoli, Gubinelli, Priola (CR29) 2011; 121 Wang (CR5) 2018; 128 CR4 CR6 CR8 CR7 Bao, Ren, Wang (CR1) 2021; 282 CR9 CR48 Zhu, Liu, Mi (CR40) 2020; 199 Tang (CR26) 2018; 50 Himonas, Kenig (CR49) 2009; 22 Miao, Rohde, Tang (CR16) 2023 Constantin, Lannes (CR35) 2009; 192 CR43 CR41 Fedrizzi, Flandoli (CR11) 2013; 264 Camassa, Holm (CR33) 1993; 71 Brzeźniak, Maslowski, Seidler (CR31) 2005; 132 Tang, Wang (CR28) 2023 CR19 CR17 Huang, Wang (CR47) 2019; 129 Da Prato (CR23) 2004 CR15 CR14 CR12 CR10 Röckner, Zhu, Zhu (CR25) 2014; 124 Huang, Röckner, Wang (CR2) 2019; 39 Holm, Staley (CR34) 2003; 308 Glatt-Holtz, Vicol (CR24) 2014; 42 Flandoli, Gubinelli, Priola (CR13) 2010; 180 Neves, Olivera (CR18) 2015; 22 Kenig, Ponce, Vega (CR50) 1991; 4 Ren (CR46) 2023; 156 Ren, Wang (CR3) 2019; 267 Li, Liu, Tang (CR27) 2021; 135 CR21 CR20 Constantin, Escher (CR38) 1998; 181 E Pardoux (10113_CR22) 1972; 275 10113_CR4 E Fedrizzi (10113_CR11) 2013; 264 10113_CR9 10113_CR8 X Huang (10113_CR47) 2019; 129 10113_CR7 A Constantin (10113_CR38) 1998; 181 10113_CR6 HR Dullin (10113_CR36) 2001; 87 P Ren (10113_CR46) 2023; 156 F Flandoli (10113_CR13) 2010; 180 H Holden (10113_CR44) 2023; 43 10113_CR48 A Himonas (10113_CR49) 2009; 22 J Bao (10113_CR1) 2021; 282 H Tang (10113_CR26) 2018; 50 10113_CR43 10113_CR41 A Constantin (10113_CR35) 2009; 192 R Camassa (10113_CR33) 1993; 71 H Tang (10113_CR45) 2023; 59 Z Brzeźniak (10113_CR31) 2005; 132 Y Miao (10113_CR16) 2023 A Constantin (10113_CR39) 1998; 51 10113_CR37 10113_CR32 10113_CR30 P Ren (10113_CR3) 2019; 267 H Tang (10113_CR28) 2023 F Flandoli (10113_CR29) 2011; 121 N Glatt-Holtz (10113_CR24) 2014; 42 M Zhu (10113_CR40) 2020; 199 10113_CR19 10113_CR17 X Huang (10113_CR2) 2019; 39 10113_CR21 10113_CR20 F-Y Wang (10113_CR5) 2018; 128 Y Chen (10113_CR42) 2021; 19 J Li (10113_CR27) 2021; 135 M Röckner (10113_CR25) 2014; 124 10113_CR15 10113_CR14 10113_CR12 10113_CR10 G Da Prato (10113_CR23) 2004 W Neves (10113_CR18) 2015; 22 DD Holm (10113_CR34) 2003; 308 CE Kenig (10113_CR50) 1991; 4 |
| References_xml | – volume: 121 start-page: 1445 year: 2011 end-page: 1463 ident: CR29 article-title: Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2011.03.004 – volume: 71 start-page: 1661 issue: 11 year: 1993 end-page: 1664 ident: CR33 article-title: An integrable shallow water equation with peaked solitons publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.71.1661 – ident: CR4 – volume: 59 start-page: 378 issue: 1 year: 2023 end-page: 410 ident: CR45 article-title: Noise effects in some stochastic evolution equations: global existence and dependence on initial data publication-title: Ann. Inst. Henri Poincaré Probab. Stat. doi: 10.1214/21-AIHP1241 – ident: CR12 – volume: 39 start-page: 3017 year: 2019 end-page: 3035 ident: CR2 article-title: Nonlinear Fokker-Planck equations for probability measures on path space and path-distribution dependent SDEs publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2019125 – ident: CR8 – volume: 50 start-page: 1322 issue: 1 year: 2018 end-page: 1366 ident: CR26 article-title: On the pathwise solutions to the Camassa-Holm equation with multiplicative noise publication-title: SIAM J. Math. Anal. doi: 10.1137/16M1080537 – ident: CR21 – ident: CR19 – volume: 42 start-page: 80 issue: 1 year: 2014 end-page: 145 ident: CR24 article-title: Local and global existence of smooth solutions for the stochastic Euler equations with multiplicative noise publication-title: Ann. Probab. doi: 10.1214/12-AOP773 – ident: CR15 – volume: 124 start-page: 1974 year: 2014 end-page: 2002 ident: CR25 article-title: Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2014.01.010 – ident: CR9 – volume: 129 start-page: 4747 year: 2019 end-page: 4770 ident: CR47 article-title: Distribution dependent SDEs with singular coefficients publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2018.12.012 – ident: CR32 – volume: 132 start-page: 119 issue: 1 year: 2005 end-page: 149 ident: CR31 article-title: Stochastic nonlinear beam equations publication-title: Probab. Theory Related Fields doi: 10.1007/s00440-004-0392-5 – volume: 267 start-page: 4745 year: 2019 end-page: 4777 ident: CR3 article-title: Bismut formula for Lions derivative of distribution dependent SDEs and applications publication-title: J. Differential Euqations doi: 10.1016/j.jde.2019.05.016 – volume: 4 start-page: 323 issue: 2 year: 1991 end-page: 347 ident: CR50 article-title: Well-posedness of the initial value problem for the Korteweg-de Vries equation publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-1991-1086966-0 – year: 2023 ident: CR16 article-title: Well-posedness for a stochastic Camassa-Holm type equation with higher order nonlinearities publication-title: Stoch. Partial Differ. Equ. Anal. Comput. doi: 10.1007/s40072-023-00291-z – volume: 192 start-page: 165 issue: 1 year: 2009 end-page: 186 ident: CR35 article-title: The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-008-0128-2 – ident: CR43 – volume: 282 start-page: 285 year: 2021 end-page: 329 ident: CR1 article-title: Bismut formulas for Lions derivative of McKean-Vlasov SDEs with memory publication-title: J. Differential Equations doi: 10.1016/j.jde.2021.02.019 – ident: CR14 – ident: CR37 – ident: CR30 – volume: 308 start-page: 437 issue: 5–6 year: 2003 end-page: 444 ident: CR34 article-title: Nonlinear balance and exchange of stability of dynamics of solitons, peakons, ramps/cliffs and leftons in a nonlinear evolutionary PDE publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(03)00114-2 – ident: CR10 – volume: 135 start-page: 139 year: 2021 end-page: 182 ident: CR27 article-title: Stochastic MHD equations with fractional kinematic dissipation and partial magnetic diffusion in publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2021.01.008 – volume: 199 start-page: 355 year: 2020 end-page: 377 ident: CR40 article-title: Wave-breaking phenomena and persistence properties for the nonlocal rotation-Camassa-Holm equation publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-019-00882-5 – ident: CR6 – year: 2023 ident: CR28 article-title: Strong solutions to nonlinear stochastic aggregation-diffusion equations publication-title: Commun. Contemp. Math. doi: 10.1142/S0219199722500730 – volume: 264 start-page: 1329 issue: 6 year: 2013 end-page: 1354 ident: CR11 article-title: Noise prevents singularities in linear transport equations publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2013.01.003 – volume: 181 start-page: 229 issue: 2 year: 1998 end-page: 243 ident: CR38 article-title: Wave breaking for nonlinear nonlocal shallow water equations publication-title: Acta Math. doi: 10.1007/BF02392586 – volume: 51 start-page: 475 issue: 5 year: 1998 end-page: 504 ident: CR39 article-title: Well-posedness, global existence, and blowup phenomena for a periodic quasi-linear hyperbolic equation publication-title: Comm. Pure Appl. Math. doi: 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO;2-5 – ident: CR48 – volume: 43 start-page: 568 issue: 2 year: 2023 end-page: 618 ident: CR44 article-title: Global well-posedness of the viscous Camassa-Holm equation with gradient noise publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2022163 – volume: 156 start-page: 291 year: 2023 end-page: 311 ident: CR46 article-title: Singular McKean-Vlasov SDEs: well-posedness, regularities and Wang’s Harnack inequality publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2022.11.010 – volume: 180 start-page: 1 issue: 1 year: 2010 end-page: 53 ident: CR13 article-title: Well-posedness of the transport equation by stochastic perturbation publication-title: Invent. Math. doi: 10.1007/s00222-009-0224-4 – ident: CR17 – volume: 22 start-page: 1247 year: 2015 end-page: 1258 ident: CR18 article-title: Wellposedness for stochastic continuity equations with Ladyzhenskaya-Prodi-Serrin condition publication-title: NoDEA Nonlinear Differential Equations Appl. doi: 10.1007/s00030-015-0321-6 – year: 2004 ident: CR23 publication-title: Kolmogorov Equations for Stochastic PDEs doi: 10.1007/978-3-0348-7909-5 – volume: 128 start-page: 595 year: 2018 end-page: 621 ident: CR5 article-title: Distribution dependent SDEs for Landau type equations publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2017.05.006 – volume: 19 start-page: 607 issue: 3 year: 2021 end-page: 627 ident: CR42 article-title: Global well-posedness of the stochastic Camassa-Holm equation publication-title: Commun. Math. Sci. doi: 10.4310/CMS.2021.v19.n3.a2 – volume: 22 start-page: 201 year: 2009 end-page: 224 ident: CR49 article-title: Non-uniform dependence on initial data for the CH equation on the line publication-title: Diff. Integr. Eqns. – ident: CR7 – volume: 87 start-page: 194501 year: 2001 ident: CR36 article-title: An integrable shallow water equation with linear and nonlinear dispersion publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.87.194501 – volume: 275 start-page: A101 year: 1972 end-page: A103 ident: CR22 article-title: Sur des equations aux dérivées partielles stochastiques monotones publication-title: C. R. Acad. Sci. – ident: CR41 – ident: CR20 – volume: 124 start-page: 1974 year: 2014 ident: 10113_CR25 publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2014.01.010 – volume: 267 start-page: 4745 year: 2019 ident: 10113_CR3 publication-title: J. Differential Euqations doi: 10.1016/j.jde.2019.05.016 – ident: 10113_CR6 doi: 10.1007/s00028-023-00890-2 – volume: 129 start-page: 4747 year: 2019 ident: 10113_CR47 publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2018.12.012 – year: 2023 ident: 10113_CR28 publication-title: Commun. Contemp. Math. doi: 10.1142/S0219199722500730 – ident: 10113_CR12 doi: 10.2422/2036-2145.201512_008 – volume: 135 start-page: 139 year: 2021 ident: 10113_CR27 publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2021.01.008 – volume: 181 start-page: 229 issue: 2 year: 1998 ident: 10113_CR38 publication-title: Acta Math. doi: 10.1007/BF02392586 – volume: 282 start-page: 285 year: 2021 ident: 10113_CR1 publication-title: J. Differential Equations doi: 10.1016/j.jde.2021.02.019 – ident: 10113_CR4 doi: 10.1016/j.jmaa.2021.125000 – ident: 10113_CR10 doi: 10.1017/CBO9781139137119 – volume: 275 start-page: A101 year: 1972 ident: 10113_CR22 publication-title: C. R. Acad. Sci. – volume: 264 start-page: 1329 issue: 6 year: 2013 ident: 10113_CR11 publication-title: J. Funct. Anal. doi: 10.1016/j.jfa.2013.01.003 – volume: 22 start-page: 201 year: 2009 ident: 10113_CR49 publication-title: Diff. Integr. Eqns. – volume: 71 start-page: 1661 issue: 11 year: 1993 ident: 10113_CR33 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.71.1661 – volume: 59 start-page: 378 issue: 1 year: 2023 ident: 10113_CR45 publication-title: Ann. Inst. Henri Poincaré Probab. Stat. doi: 10.1214/21-AIHP1241 – year: 2023 ident: 10113_CR16 publication-title: Stoch. Partial Differ. Equ. Anal. Comput. doi: 10.1007/s40072-023-00291-z – volume: 156 start-page: 291 year: 2023 ident: 10113_CR46 publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2022.11.010 – ident: 10113_CR7 doi: 10.1007/978-3-642-36297-2_2 – volume: 180 start-page: 1 issue: 1 year: 2010 ident: 10113_CR13 publication-title: Invent. Math. doi: 10.1007/s00222-009-0224-4 – volume: 192 start-page: 165 issue: 1 year: 2009 ident: 10113_CR35 publication-title: Arch. Ration. Mech. Anal. doi: 10.1007/s00205-008-0128-2 – ident: 10113_CR9 doi: 10.1515/9783110492552 – volume: 308 start-page: 437 issue: 5–6 year: 2003 ident: 10113_CR34 publication-title: Phys. Lett. A doi: 10.1016/S0375-9601(03)00114-2 – ident: 10113_CR43 – ident: 10113_CR19 doi: 10.1017/CBO9781107295513 – volume: 43 start-page: 568 issue: 2 year: 2023 ident: 10113_CR44 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2022163 – ident: 10113_CR48 doi: 10.1214/ECP.v19-2833 – volume: 132 start-page: 119 issue: 1 year: 2005 ident: 10113_CR31 publication-title: Probab. Theory Related Fields doi: 10.1007/s00440-004-0392-5 – volume: 128 start-page: 595 year: 2018 ident: 10113_CR5 publication-title: Stoch. Proc. Appl. doi: 10.1016/j.spa.2017.05.006 – volume: 22 start-page: 1247 year: 2015 ident: 10113_CR18 publication-title: NoDEA Nonlinear Differential Equations Appl. doi: 10.1007/s00030-015-0321-6 – ident: 10113_CR21 – ident: 10113_CR37 doi: 10.1007/s00021-019-0432-7 – volume: 51 start-page: 475 issue: 5 year: 1998 ident: 10113_CR39 publication-title: Comm. Pure Appl. Math. doi: 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO;2-5 – ident: 10113_CR41 doi: 10.1007/s00332-021-09755-9 – volume: 39 start-page: 3017 year: 2019 ident: 10113_CR2 publication-title: Discrete Contin. Dyn. Syst. doi: 10.3934/dcds.2019125 – volume-title: Kolmogorov Equations for Stochastic PDEs year: 2004 ident: 10113_CR23 doi: 10.1007/978-3-0348-7909-5 – ident: 10113_CR15 doi: 10.1007/s00030-019-0602-6 – ident: 10113_CR30 – volume: 4 start-page: 323 issue: 2 year: 1991 ident: 10113_CR50 publication-title: J. Amer. Math. Soc. doi: 10.1090/S0894-0347-1991-1086966-0 – ident: 10113_CR14 doi: 10.1007/s10231-017-0633-8 – ident: 10113_CR8 doi: 10.1007/978-3-642-18231-0 – volume: 199 start-page: 355 year: 2020 ident: 10113_CR40 publication-title: Ann. Mat. Pura Appl. doi: 10.1007/s10231-019-00882-5 – ident: 10113_CR17 doi: 10.1016/j.jfa.2023.110075 – volume: 50 start-page: 1322 issue: 1 year: 2018 ident: 10113_CR26 publication-title: SIAM J. Math. Anal. doi: 10.1137/16M1080537 – ident: 10113_CR20 – volume: 19 start-page: 607 issue: 3 year: 2021 ident: 10113_CR42 publication-title: Commun. Math. Sci. doi: 10.4310/CMS.2021.v19.n3.a2 – volume: 87 start-page: 194501 year: 2001 ident: 10113_CR36 publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.87.194501 – volume: 42 start-page: 80 issue: 1 year: 2014 ident: 10113_CR24 publication-title: Ann. Probab. doi: 10.1214/12-AOP773 – ident: 10113_CR32 doi: 10.1016/0167-2789(81)90004-X – volume: 121 start-page: 1445 year: 2011 ident: 10113_CR29 publication-title: Stochastic Process. Appl. doi: 10.1016/j.spa.2011.03.004 |
| SSID | ssj0002778 |
| Score | 2.3767252 |
| Snippet | By using a regularity approximation argument, the global existence and uniqueness are derived for a class of nonlinear SPDEs depending on both the whole... |
| SourceID | cristin proquest crossref springer |
| SourceType | Open Access Repository Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 379 |
| SubjectTerms | Coriolis effect Fluid dynamics Fluid mechanics Functional Analysis Geometry Mathematics Mathematics and Statistics Partial differential equations Potential Theory Probability Theory and Stochastic Processes Uniqueness Wave breaking |
| Title | Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations |
| URI | https://link.springer.com/article/10.1007/s11118-023-10113-5 https://www.proquest.com/docview/3086030213 http://hdl.handle.net/10852/117655 |
| Volume | 61 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVLSH databaseName: SpringerLink Journals customDbUrl: mediaType: online eissn: 1572-929X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002778 issn: 0926-2601 databaseCode: AFBBN dateStart: 19920301 isFulltext: true providerName: Library Specific Holdings – providerCode: PRVAVX databaseName: SpringerLINK - Czech Republic Consortium customDbUrl: eissn: 1572-929X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002778 issn: 0926-2601 databaseCode: AGYKE dateStart: 19970101 isFulltext: true titleUrlDefault: http://link.springer.com providerName: Springer Nature – providerCode: PRVAVX databaseName: SpringerLink Journals (ICM) customDbUrl: eissn: 1572-929X dateEnd: 99991231 omitProxy: true ssIdentifier: ssj0002778 issn: 0926-2601 databaseCode: U2A dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.springerlink.com/journals/ providerName: Springer Nature |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlZ3PT4MwFMcb3S56MP6M6Fx68KaNUGiBI_vlotmyZC6ZJwKlxINhOvD_9xU60EVNvEBIgUMf773vo-2nCF2DAvWpTFwizNgkDjVjEjuRQyCZWJBRRGKXq_gnUz5eOA9LttSYHLUWZmv8_i5XLu0RyCwQMCzLJmwXtRkEXjV9r8_7ddSlbhV1fcqJwmTpBTI_vwPErih9KPuejhqNuTUsWmab0SE60DIRB5Vdj9COzI7R_hd4IFxNauJqfoLEQBFw9eZVZAZNeKD3ty3wtOJhRGs8nw2GOVY_X3HQDF3jYoXnxUq8RIrajGvgOVZVKh6-Vzjw_BQtRsOn_pjoDRSIsD2vIJYEd_VBU8HZTCWXCfM94YOCEFBopZ6TKDYLZwLqwtSXqctTy0x4KngSpZGk9hlqZatMniNseb7wKdR-DCpKUFkRdb2SLSaS2HYjYSBD92iYwberuKOMKpI4Z8xA1qaPQ6HJ42oDjNewYSYrC4VgobC0UAjP3NTPvFXcjT_v7mxMF2ofzEMbqjUIYdSyDXS7MWfT_PvbLv53-yXao6B0qlmBHdQq1h_yCpRKEXdROxj1elN1vn9-HHbLTxaOCxp8AlYb3gM |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3NT9swFH8a5QAcYBtMFNjwYbdhFDtfzrGi7bpBq0ptJThZieMIaSiFJlz463lOnIahMYlcosgfSmy_934v9vs9gO-IQCOu05AqJ3Gox52EJl7sUTQmDC2KSt0qin88CUYL7_e1f22DwormtHuzJVlp6jbYDS9B0cag6mDMpf4GbHpMCK8Dm72fN5eDtQbmYa2BIx5QQ5llg2X-3QsCX1XJU_63aWrx5qst0sryDPdg0bxzfeDkz_ljmZyrp1d0ju_9qI-wa6Eo6dVr5xN80Pln2HlBUIhP4zWra7EPqm9Ydm2CLDrFItK3OXRLMqk5N-IVmU37g4KYH7yk126Pk3JJZuVS3caGGZqsSdWJ8YTJ4KGmHC8OYDEczC9G1CZpoMoVoqRMo0qIELfh3cl0oFM_EipClKLQmcuElxr-l8BX6Htmkc7CIGNOGmQqSOMs1tz9Ap18metDIExEKuLoX_rotSKSi3koKv4ylSZuGKsudO1MyRzlw3Cb-tywlQe-3wXWzJ1Ult3cJNm4ky0vsxlqiUMtq6GW2ObHus19ze3x39onzZKQVs4L6aJHiGqSM7cLZ80Mt8Vv93b0vuqnsDWaj6_k1a_J5TFsc0RW9SnEE-iUq0f9FZFRmXyzgvAMSKn-Bw |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlZ3PT4MwFMcbnYnRg_FnRKf24E0bofw-LrJl_tiyZC7ZrYHSxoNhc-D_7ysUmEZN5EIItIc--t73Ud6nCF2DAg2pSH3CzcQkDjUTkjixQyCYWBBReGqXVfyjsTecOY9zd75WxV_-7V4vSVY1DYrSlBV3y1TetYVvcAQE4g24EcuyibuJthyI1Sr9mtFe44upX_nikHpEwbN02czPfYAE5uXMyr4GqVZ5flssLWPQYB_tafGIe5W1D9CGyA7R7hpSEK5GDYc1P0I8UlxcvaUVmcAtHOldbws8rigZ8QpPJ1E_x-qTLO61C9q4WOBpseCvsWI54waDjlXuivvvFSQ8P0azQf_lfkj0tgqE20FQEEvAJA5BacHZlMITqRsGPARdwSH9koGTKmKL53LIFmUopO9Jy0w9yb00lrGg9gnqZItMnCJsBSEPKWSELuSZoL1i6gclcYynie3H3ECGHlGWwRutaKQuVXxxz3UNZNVjzLjmkattMd5YS1JWFmJgIVZaiEGbm6bNsqJx_Pl0tzYd0zMzZzbkcODYqGUb6LY2Z3v7997O_vf4FdqeRAP2_DB-Okc7FKRQ9dtgF3WK1Ye4AClTJJfl2_oJlAflXw |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Distribution-Path+Dependent+Nonlinear+SPDEs+with+Application+to+Stochastic+Transport+Type+Equations&rft.jtitle=Potential+analysis&rft.au=Ren%2C+Panpan&rft.au=Tang%2C+Hao&rft.au=Wang%2C+Feng-Yu&rft.date=2024-08-01&rft.issn=0926-2601&rft.eissn=1572-929X&rft.volume=61&rft.issue=2&rft.spage=379&rft.epage=407&rft_id=info:doi/10.1007%2Fs11118-023-10113-5&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11118_023_10113_5 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0926-2601&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0926-2601&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0926-2601&client=summon |