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Abstract and Applied Analysis
Volume 2014, Article ID 132324, 12 pages
Research Article

Global Solutions to the Spherically Symmetric Compressible Navier-Stokes Equations with Density-Dependent Viscosity and Discontinuous Initial Data

1College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China
3College of Teacher Education, Quzhou University, Quzhou 324000, China

Received 29 September 2013; Accepted 8 April 2014; Published 4 May 2014

Academic Editor: Adem Kılıçman

Copyright © 2014 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.


We consider the initial boundary value problem for the spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data in this paper. For piecewise regular initial density with bounded jump discontinuity, we show that there exists a unique global piecewise regular solution. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as .