On the free boundary value problem for one-dimensional compressible Navier-Stokes equations with constant exterior pressure
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
Boundary Value Problems 2014, 2014:93 doi:10.1186/1687-2770-2014-93Published: 6 May 2014
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.