Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment
In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreov...
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Published in | Nonlinearity Vol. 37; no. 6; pp. 65014 - 65040 |
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Format | Journal Article |
Language | English |
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03.06.2024
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ISSN | 0951-7715 1361-6544 |
DOI | 10.1088/1361-6544/ad422b |
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Abstract | In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment. |
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AbstractList | In this paper, we study the asymptotic stability of the rarefaction wave for the one-dimensional compressible Euler system with nonlocal velocity alignment. Namely, for the initial data approaching to rarefaction wave, we prove the corresponding solution converges toward the rarefaction wave. Moreover, we obtain this system has weak alignment behavior. We develop some promoted estimates for the smooth approximate rarefaction wave and new a priori estimates by Fourier analysis tools. Moreover, we introduce the weighted energy method and Besov spaces to obtain the key high-order derivative estimates, in which we overcome the difficulties caused by the nonlocal velocity alignment. It is worth mentioning that this is the first stability result of rarefaction wave for compressible Euler system with velocity alignment. |
Author | Bai, Xiang Xu, Xiaojing Li, Lin-An |
Author_xml | – sequence: 1 givenname: Xiang orcidid: 0000-0003-0006-1287 surname: Bai fullname: Bai, Xiang organization: Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing 100190, People’s Republic of China – sequence: 2 givenname: Lin-An orcidid: 0000-0003-0937-7843 surname: Li fullname: Li, Lin-An organization: School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University , Beijing 100875, People’s Republic of China – sequence: 3 givenname: Xiaojing surname: Xu fullname: Xu, Xiaojing organization: School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, MOE, Beijing Normal University , Beijing 100875, People’s Republic of China |
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Cites_doi | 10.1088/1361-6544/ad140b 10.1142/S0218202517400103 10.4171/rmi/1049 10.2140/apde.2019.12.843 10.1103/PhysRevLett.75.1226 10.1007/BF03167088 10.4310/CMS.2009.v7.n2.a2 10.1142/S0218202521500081 10.4310/CMS.2022.v20.n4.a9 10.1007/s00220-004-1055-1 10.1016/S0375-9601(00)00201-2 10.1016/j.jde.2014.05.007 10.1093/imatrm/tnx001 10.1142/S0218202522500543 10.4310/MAA.2021.v28.n2.a3 10.1098/rsta.2013.0401 10.1016/j.jde.2023.10.010 10.1016/j.jde.2021.04.002 10.1090/S0002-9947-1990-0970270-8 10.1017/S0022112095000012 10.3934/dcdsb.2021164 10.1137/S0036141096306005 10.1142/S0218202519500064 10.1142/S0218202523500021 10.1002/cpa.3160100406 10.1142/S0218202515500050 10.1109/MCS.2007.384123 10.1007/BF01466726 10.1137/090753449 10.1098/rsif.2014.0352 10.1137/S003614100342735X 10.1143/JPSJ.50.3262 10.1007/s00205-021-01676-x 10.1007/s00205-017-1184-2 10.3934/krm.2008.1.415 10.1109/JPROC.2006.887295 10.1016/j.physd.2017.09.003 10.3934/dcds.2017239 10.1137/070681776 10.1080/03605302.2022.2091454 10.1137/19M1278983 |
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Title | Asymptotic stability of rarefaction wave for compressible Euler system with velocity alignment |
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