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Open Access Research

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

Ruxu Lian12* and Jian Liu3

Author Affiliations

1 College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou, 450011, P.R. China

2 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, P.R. China

3 College of Teacher Education, Quzhou University, Quzhou, 324000, P.R. China

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Boundary Value Problems 2014, 2014:93  doi:10.1186/1687-2770-2014-93

Published: 6 May 2014

Abstract

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.

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