A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients

Local solutions of the multidimensional Navier-Stokes equations for isentropic compressible flow are constructed with spherically symmetric initial data between a solid core and a free boundary connected to a surrounding vacuum state. The viscosity coefficients $\lambda, \mu$ are proportional to $\rho^\theta}$, $0 1$ is the physical constant of polytropic fluid. It is also proved that no vacuum develops between the solid core and the free boundary, and the free boundary expands with finite speed.

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