On the free boundary value problem for one-dimensional compressible Navier-Stokes equations with constant exterior pressure

Boundary value problems

Ruxu Lian¹  Jian Liu² 

[1] College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, P.R. China;Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, P.R. China

关键词: Navier-Stokes equations;    free boundary value problem;    density-dependent viscosity coefficient;    exterior pressure;    strong solution;   

DOI  :  10.1186/1687-2770-2014-93

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we consider the free boundary value problem (FBVP) for one-dimensional isentropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficient and constant exterior pressure. Under certain assumptions imposed on the initial data, the global existence and uniqueness of a strong solution to FBVP for CNS are established, in particular, the strong solution tends pointwise to a non-vacuum equilibrium state at an exponential time-rate as the time tends to infinity.

【 授权许可】

CC BY