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In this paper, we consider the exterior problem for spherically symmetric isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficients and discontinuous initial data. We prove that there exists a unique global piecewise regular solution for piecewise regular initial density with bounded jump discontinuity. In particular, the jump of density decays exponentially in time and the piecewise regular solution tends to the equilibrium state exponentially as t → +∞. © 2013 Lian and Yang.

boundary value problems

Global solution to the exterior problem for spherically symmetric compressible Navier-Stokes equations with density-dependent viscosity and discontinuous initial data