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

Ping Chen·Ting Zhang
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Abstract

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 $λ, μ$ are proportional to $ρ^θ}$, $0<θ<γ$, where $ρ$ is the density and $γ>1$ 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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Ping Chen, Ting Zhang. 2008-04-16. A vacuum problem for multidimensional compressible Navier-Stokes equations with degenerate viscosity coefficients. https://arxiv.org/abs/math/0701150

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