Global Behavior of Spherically Symmetric Navier-Stokes Equations with Degenerate Viscosity Coefficients

Details Global Behavior of Spherically Symmetric Navier-Stokes Equations with Degenerate Viscosity Coefficients Global Behavior of Spherically Symmetric Navier-Stokes Equations with Degenerate Viscosity Coefficients

2007-02-12

arxiv.org/abs/math/0702308v2

Mathematics

Analysis of PDEs

34 pages

Scientific paper

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we obtain the global existence and uniqueness of the weak solution and give some uniform bounds (with respect to time) of the solution. Moreover, we obtain some stabilization rate estimates in $L^\infty$-norm and weighted $H^1$-norm of the solution. The results show that such system is stable under the small perturbations, and could be applied to the astrophysics.

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