Vanishing Viscosity Limit to the Planar Rarefaction Wave for the Two-Dimensional Compressible Navier-Stokes Equations

doi:10.1007/s00220-019-03580-8

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	Vanishing Viscosity Limit to the Planar Rarefaction Wave for the Two-Dimensional Compressible Navier-Stokes Equations
	Li, Lin-An 1,2; Wang, Dehua 3; Wang, Yi 1,2
刊名	COMMUNICATIONS IN MATHEMATICAL PHYSICS
	2019-09-30
页码	32
ISSN号	0010-3616
DOI	10.1007/s00220-019-03580-8
英文摘要	The vanishing viscosity limit of the two-dimensional (2D) compressible and isentropic Navier-Stokes equations is studied in the case that the corresponding 2D inviscid Euler equations admit a planar rarefaction wave solution. It is proved that there exists a family of smooth solutions for the 2D compressible Navier-Stokes equations converging to the planar rarefaction wave solution with arbitrary strength for the 2D Euler equations. A uniform convergence rate is obtained in terms of the viscosity coefficients away from the initial time. In the proof, the hyperbolic wave is crucially introduced to recover the physical viscosities of the inviscid rarefaction wave profile, in order to rigorously justify the vanishing viscosity limit.
资助项目	National Science Foundation[DMS-1312800] ; National Science Foundation[DMS-1613213] ; NSFC[11671385] ; NSFC[11688101] ; CAS Interdisciplinary Innovation Team
WOS研究方向	Physics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000496832300001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/50717]
专题	应用数学研究所
通讯作者	Li, Lin-An
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 3.Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
推荐引用方式 GB/T 7714	Li, Lin-An,Wang, Dehua,Wang, Yi. Vanishing Viscosity Limit to the Planar Rarefaction Wave for the Two-Dimensional Compressible Navier-Stokes Equations[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS,2019:32.
APA	Li, Lin-An,Wang, Dehua,&Wang, Yi.(2019).Vanishing Viscosity Limit to the Planar Rarefaction Wave for the Two-Dimensional Compressible Navier-Stokes Equations.COMMUNICATIONS IN MATHEMATICAL PHYSICS,32.
MLA	Li, Lin-An,et al."Vanishing Viscosity Limit to the Planar Rarefaction Wave for the Two-Dimensional Compressible Navier-Stokes Equations".COMMUNICATIONS IN MATHEMATICAL PHYSICS (2019):32.