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Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data
Huang, Feimin; Li, Jing; Xin, Zhouping
2006-12-01
Source PublicationJOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
ISSN0021-7824
Volume86Issue:6Pages:471-491
AbstractThis paper concerns the large time behavior of strong and classical solutions to the two-dimensional Stokes approximation equations for the compressible flows. We consider the unique global strong solution or classical solution to the two-dimensional Stokes approximation equations for the compressible flows with large external potential force, together with a Navier-slip boundary condition, for arbitrarily large initial data. Under the conditions that the corresponding steady state exists uniquely with the steady state density away from vacuum, we prove that the density is bounded from above independently of time, consequently, it converges to the steady state density in L-p and the velocity u converges to the steady state velocity in W-1.p for any 1 <= p < infinity as time goes to infinity; furthermore, we show that if the initial density contains vacuum at least at one point, then the derivatives of the density must blow up as time goes to infinity. (C) 2006 Elsevier Masson SAS. All rights reserved.
Keywordstokes approximation equations large external potential forces large-time behavior uniform upper bound vacuum blowup
DOI10.1016/j.matpur.2006.10.001
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000243143900003
PublisherGAUTHIER-VILLARS/EDITIONS ELSEVIER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/3321
Collection应用数学研究所
Corresponding AuthorHuang, Feimin
Affiliation1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China
2.Chinese Univ Hong Kong, Inst Math Sci, Shatin, Hong Kong, Peoples R China
3.Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China
Recommended Citation
GB/T 7714
Huang, Feimin,Li, Jing,Xin, Zhouping. Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,2006,86(6):471-491.
APA Huang, Feimin,Li, Jing,&Xin, Zhouping.(2006).Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data.JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES,86(6),471-491.
MLA Huang, Feimin,et al."Convergence to equilibria and blowup behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows with large data".JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES 86.6(2006):471-491.
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