Contact discontinuity with general perturbations for gas motions

doi:10.1016/j.aim.2008.06.014

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	Contact discontinuity with general perturbations for gas motions
	Huang, Feimin1 ; Xin, Zhouping 2; Yang, Tong 3
	2008-11-10
发表期刊	ADVANCES IN MATHEMATICS
ISSN	0001-8708
卷号	219 期号:4 页码:1246-1297
摘要	The contact discontinuity is one of the basic wave patterns in gas motions. The stability of contact discontinuities with general perturbations for the Navier-Stokes equations and the Boltzmann equation is a long standing open problem. General perturbations of a contact discontinuity may generate diffusion waves which evolve and interact with the contact wave to cause analytic difficulties. In this paper, we succeed in obtaining the large time asymptotic stability of a contact wave pattern with a convergence rate for the Navier-Stokes equations and the Boltzmann equation in a uniform way. One of the key observations is that even though the energy norm of the deviation of the solution from the contact wave may grow at the rate (1 + t)(1/4), it can be compensated by the decay in the energy norm of the derivatives of the deviation which is of the order of (1 + t)-(1/4). Thus, this reciprocal order of decay rates for the time evolution of the perturbation is essential to close the a priori estimate containing the uniform bounds of the L-infinity norm on the lower order estimate and then it gives the decay of the solution to the contact wave pattern. (C) 2008 Elsevier Inc. All rights reserved.
关键词	contact discontinuity stability compressible Navier-Stokes equations Boltzmann equation
DOI	10.1016/j.aim.2008.06.014
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000259652400004
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/6025
专题	应用数学研究所
通讯作者	Huang, Feimin
作者单位	1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China 3.City Univ Hong Kong, Lie Bie Ju Ctr Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Huang, Feimin,Xin, Zhouping,Yang, Tong. Contact discontinuity with general perturbations for gas motions[J]. ADVANCES IN MATHEMATICS,2008,219(4):1246-1297.
APA	Huang, Feimin,Xin, Zhouping,&Yang, Tong.(2008).Contact discontinuity with general perturbations for gas motions.ADVANCES IN MATHEMATICS,219(4),1246-1297.
MLA	Huang, Feimin,et al."Contact discontinuity with general perturbations for gas motions".ADVANCES IN MATHEMATICS 219.4(2008):1246-1297.