TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN
This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry...
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| Published in | Acta mathematica scientia Vol. 36; no. 4; pp. 1015 - 1029 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.07.2016
School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China%Department of Mathematics, City University of Hong Kong, Hong Kong, China |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(16)30055-8 |
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| Abstract | This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given. |
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| AbstractList | This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given. |
| Author | 金春花 杨彤 |
| AuthorAffiliation | School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China Department of Mathematics, City University of Hong Kong, Hong Kong, China |
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| CitedBy_id | crossref_primary_10_1002_mma_4592 crossref_primary_10_1007_s10114_020_9413_2 crossref_primary_10_1007_s00033_020_01409_2 crossref_primary_10_1007_s10473_019_0206_6 crossref_primary_10_1016_j_jmaa_2020_124146 crossref_primary_10_1007_s00033_017_0782_z crossref_primary_10_1002_mma_7615 crossref_primary_10_1007_s10473_024_0310_0 |
| Cites_doi | 10.1088/0951-7715/4/2/013 10.2748/tmj/1178225411 10.1007/s11565-010-0108-y 10.1007/BF00284169 10.1016/j.jde.2013.04.036 10.1007/BF00253153 10.1142/S0218202512500078 10.1007/s00205-012-0492-9 10.1016/j.jde.2009.11.031 |
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| Copyright | 2016 Wuhan Institute of Physics and Mathematics Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| DocumentTitleAlternate | TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN |
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| GrantInformation_xml | – fundername: Pearl River S&T Nova Program of Guangzhou grantid: 2013J2200064 – fundername: NSFC grantid: 11471127 – fundername: C. Jin's research is supported by the Program for New Century Excellent Talents in University of the Ministry of Education grantid: NCET-13-0804 – fundername: Guangdong Natural Science Funds for Distinguished Young Scholar grantid: 2015A030306029 – fundername: The Excellent Young Teachers Program of Guangdong Province grantid: HS2015007 – fundername: Special support program of Guangdong Province; T. Yang is supported by the General Research Fund of Hong Kong, CityU grantid: 104511 – fundername: C.Jin's research is supported by the Program for New Century Excellent Talents in University of the Ministry of Education; NSFC; Guangdong Natural Science Funds for Distinguished Young Scholar; The Excellent Young Teachers Program of Guangdong Province; Pearl River S&T Nova Program of Guangzhou; Special support program of Guangdong Province; T.Yang is supported by the General Research Fund of Hong Kong,CityU 104511 funderid: (NCET-13-0804); (11471127); (2015A030306029); (HS2015007); (2013J2200064); Special support program of Guangdong Province; T.Yang is supported by the General Research Fund of Hong Kong,CityU 104511 |
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| Keywords | energy method Time periodic solution 35B10 topology degree 35Q30 compressible Navier-Stokes equation 35M10 |
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| Notes | Time periodic solution; compressible Navier-Stokes equation; topology degree; energy method 42-1227/O This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| References | Maremonti (bib6) 1991; 4 Farwig, Okabe (bib5) 2010; 56 Valli (bib9) 1983; 10 Matsumura, Nishida (bib10) 1989; 10 Yudovich (bib2) 1960; 1 Ma, Ukai, Yang (bib14) 2010; 248 Feireisl, Mucha, Novotny, Pokorny (bib11) 2012; 204 Březina, Kagei (bib12) 2012; 22 Březina, Kagei (bib13) 2013; 255 Prodi (bib3) 1960; 30 Serrin (bib1) 1959; 3 Maremonti (bib7) 1991; 40 Kaniel, Shinbrot (bib4) 1967; 24 Kozono, Nakao (bib8) 1996; 48 Kozono (10.1016/S0252-9602(16)30055-8_bib8) 1996; 48 Březina (10.1016/S0252-9602(16)30055-8_bib13) 2013; 255 Serrin (10.1016/S0252-9602(16)30055-8_bib1) 1959; 3 Valli (10.1016/S0252-9602(16)30055-8_bib9) 1983; 10 Prodi (10.1016/S0252-9602(16)30055-8_bib3) 1960; 30 Matsumura (10.1016/S0252-9602(16)30055-8_bib10) 1989; 10 Ma (10.1016/S0252-9602(16)30055-8_bib14) 2010; 248 Kaniel (10.1016/S0252-9602(16)30055-8_bib4) 1967; 24 Březina (10.1016/S0252-9602(16)30055-8_bib12) 2012; 22 Maremonti (10.1016/S0252-9602(16)30055-8_bib6) 1991; 4 Farwig (10.1016/S0252-9602(16)30055-8_bib5) 2010; 56 Yudovich (10.1016/S0252-9602(16)30055-8_bib2) 1960; 1 Maremonti (10.1016/S0252-9602(16)30055-8_bib7) 1991; 40 Feireisl (10.1016/S0252-9602(16)30055-8_bib11) 2012; 204 |
| References_xml | – volume: 3 start-page: 120 year: 1959 end-page: 122 ident: bib1 article-title: A note on the existence of periodic solutions of the Navier-Stokes equations publication-title: Arch Rational Mech Anal – volume: 10 start-page: 49 year: 1989 end-page: 82 ident: bib10 article-title: Periodic solutions of a viscous gas equation. Recent topics in nonlinear PDE IV (Kyoto, 1988) publication-title: Lecture Notes in Num Appl Anal – volume: 10 start-page: 607 year: 1983 end-page: 647 ident: bib9 article-title: Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method publication-title: Ann Scuola Norm Sup Pisa Cl Sci – volume: 30 start-page: 1 year: 1960 end-page: 15 ident: bib3 article-title: Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso bidimensionale publication-title: Rend Sem Mat Univ Padova – volume: 48 start-page: 33 year: 1996 end-page: 50 ident: bib8 article-title: Periodic solutions of the Navier-Stokes equations in unbounded domains publication-title: Tohoku Math J – volume: 22 start-page: 1 year: 2012 end-page: 53 ident: bib12 article-title: Decay properties of solutions to the linearized compressible navier-stokes equation around time-periodic parallel flow publication-title: Mathematical Models and Methods in Applied Sciences – volume: 40 start-page: 81 year: 1991 end-page: 135 ident: bib7 article-title: Some theorems of existence for solutions of the Navier-Stokes equations with slip boundary conditions in half-space publication-title: Rich Mat – volume: 56 start-page: 249 year: 2010 end-page: 281 ident: bib5 article-title: Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions publication-title: Ann Univ Ferrara – volume: 204 start-page: 745 year: 2012 end-page: 786 ident: bib11 article-title: Time-Periodic Solutions to the Full Navier-Stokes-Fourier System publication-title: Arch Rational Mech Anal – volume: 24 start-page: 265 year: 1967 end-page: 288 ident: bib4 article-title: A Reproductive Property of the Navier-Stokes Equations publication-title: Arch Rational Mech Anal – volume: 255 start-page: 1132 year: 2013 end-page: 1195 ident: bib13 article-title: Spectral properties of the linearized compressible Navier-Stokes equation around time-periodic parallel flow publication-title: J Differential Equations – volume: 248 start-page: 2275 year: 2010 end-page: 2293 ident: bib14 article-title: Time periodic solutions of compressible Navier-Stokes equations publication-title: J Differential Equations – volume: 4 start-page: 503 year: 1991 end-page: 529 ident: bib6 article-title: Existence and stability of time periodic solution of the Navier-Stokes equations in the whole space publication-title: Nonlinearity – volume: 1 start-page: 1214 year: 1960 end-page: 1217 ident: bib2 article-title: Periodic motions of a viscous incompressible fluid publication-title: Soviet Math – volume: 4 start-page: 503 year: 1991 ident: 10.1016/S0252-9602(16)30055-8_bib6 article-title: Existence and stability of time periodic solution of the Navier-Stokes equations in the whole space publication-title: Nonlinearity doi: 10.1088/0951-7715/4/2/013 – volume: 10 start-page: 607 issue: 4 year: 1983 ident: 10.1016/S0252-9602(16)30055-8_bib9 article-title: Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method publication-title: Ann Scuola Norm Sup Pisa Cl Sci – volume: 30 start-page: 1 year: 1960 ident: 10.1016/S0252-9602(16)30055-8_bib3 article-title: Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso bidimensionale publication-title: Rend Sem Mat Univ Padova – volume: 48 start-page: 33 year: 1996 ident: 10.1016/S0252-9602(16)30055-8_bib8 article-title: Periodic solutions of the Navier-Stokes equations in unbounded domains publication-title: Tohoku Math J doi: 10.2748/tmj/1178225411 – volume: 56 start-page: 249 year: 2010 ident: 10.1016/S0252-9602(16)30055-8_bib5 article-title: Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions publication-title: Ann Univ Ferrara doi: 10.1007/s11565-010-0108-y – volume: 3 start-page: 120 year: 1959 ident: 10.1016/S0252-9602(16)30055-8_bib1 article-title: A note on the existence of periodic solutions of the Navier-Stokes equations publication-title: Arch Rational Mech Anal doi: 10.1007/BF00284169 – volume: 1 start-page: 1214 year: 1960 ident: 10.1016/S0252-9602(16)30055-8_bib2 article-title: Periodic motions of a viscous incompressible fluid publication-title: Soviet Math – volume: 255 start-page: 1132 year: 2013 ident: 10.1016/S0252-9602(16)30055-8_bib13 article-title: Spectral properties of the linearized compressible Navier-Stokes equation around time-periodic parallel flow publication-title: J Differential Equations doi: 10.1016/j.jde.2013.04.036 – volume: 24 start-page: 265 year: 1967 ident: 10.1016/S0252-9602(16)30055-8_bib4 article-title: A Reproductive Property of the Navier-Stokes Equations publication-title: Arch Rational Mech Anal doi: 10.1007/BF00253153 – volume: 40 start-page: 81 year: 1991 ident: 10.1016/S0252-9602(16)30055-8_bib7 article-title: Some theorems of existence for solutions of the Navier-Stokes equations with slip boundary conditions in half-space publication-title: Rich Mat – volume: 22 start-page: 1 year: 2012 ident: 10.1016/S0252-9602(16)30055-8_bib12 article-title: Decay properties of solutions to the linearized compressible navier-stokes equation around time-periodic parallel flow publication-title: Mathematical Models and Methods in Applied Sciences doi: 10.1142/S0218202512500078 – volume: 10 start-page: 49 year: 1989 ident: 10.1016/S0252-9602(16)30055-8_bib10 article-title: Periodic solutions of a viscous gas equation. Recent topics in nonlinear PDE IV (Kyoto, 1988) publication-title: Lecture Notes in Num Appl Anal – volume: 204 start-page: 745 year: 2012 ident: 10.1016/S0252-9602(16)30055-8_bib11 article-title: Time-Periodic Solutions to the Full Navier-Stokes-Fourier System publication-title: Arch Rational Mech Anal doi: 10.1007/s00205-012-0492-9 – volume: 248 start-page: 2275 year: 2010 ident: 10.1016/S0252-9602(16)30055-8_bib14 article-title: Time periodic solutions of compressible Navier-Stokes equations publication-title: J Differential Equations doi: 10.1016/j.jde.2009.11.031 |
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| SubjectTerms | 35B10 35M10 35Q30 Compressibility compressible Navier-Stokes equation Constraining energy method Mathematical analysis Navier-Stokes equations Regularization Symmetry Time periodic solution topology degree Uniqueness 可压缩Navier-Stokes方程 外力 抛物 时间周期解 正则化方法 等熵压缩 解的存在性 |
| Title | TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN |
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