Journal of Applied Mathematics
Volume 2012 (2012), Article ID 395209, 22 pages
http://dx.doi.org/10.1155/2012/395209
Research Article

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity

Ruxu Lian,1 Lan Huang,1 and Jian Liu2

1College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2Department of Mathematics, Capital Normal University, Beijing 100048, China

Received 20 December 2011; Revised 21 March 2012; Accepted 31 March 2012

Academic Editor: Nazim I. Mahmudov

Copyright © 2012 Ruxu Lian et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the exterior problem and the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient in this paper. For regular initial density, we show that there exists a unique global strong solution to the exterior problem or the initial boundary value problem, respectively. In particular, the strong solution tends to the equilibrium state as 𝑡 → + ∞ .