Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Isentropic Navier-Stokes Equations

doi:10.1007/s00220-021-04203-x

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	Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Isentropic Navier-Stokes Equations
	Huang, Feimin 1,2; Yuan, Qian 1
刊名	COMMUNICATIONS IN MATHEMATICAL PHYSICS
	2021-08-26
页码	25
ISSN号	0010-3616
DOI	10.1007/s00220-021-04203-x
英文摘要	The stability of solutions under periodic perturbations for both inviscid and viscous conservation laws is an interesting and important problem. In this paper, a large-amplitude viscous shock under space-periodic perturbation for the isentropic Navier-Stokes equations is considered. It is shown that if the initial perturbation around the shock is suitably small and satisfies a zero-mass type condition (2.17), then the solution of the N-S equations tends to the viscous shock with a shift, which is partially determined by the periodic oscillations. In other words, the viscous shock is nonlinearly stable even though the perturbation oscillates at the far fields. The key point is to construct a suitable ansatz ((v) over tilde, (u) over tilde), which carries the same oscillations of the solution (v, u) at the far fields, so that the difference (v - (v) over tilde, u - (u) over tilde) belongs to the H-2(R) space for all t >= 0.
资助项目	China Postdoctoral Science Foundation[11371349] ; China Postdoctoral Science Foundation[11688101] ; [2019M660831] ; [2020TQ0345]
WOS研究方向	Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000689507700001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59153]
专题	应用数学研究所
通讯作者	Huang, Feimin
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Yuan, Qian. Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Isentropic Navier-Stokes Equations[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2021:25.
APA	Huang, Feimin,&Yuan, Qian.(2021).Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Isentropic Navier-Stokes Equations.COMMUNICATIONS IN MATHEMATICAL PHYSICS,25.
MLA	Huang, Feimin,et al."Stability of Large-Amplitude Viscous Shock Under Periodic Perturbation for 1-d Isentropic Navier-Stokes Equations".COMMUNICATIONS IN MATHEMATICAL PHYSICS (2021):25.