### On Spherically Symmetric Solutions of the Compressible Isentropic Navier-Stokes Equations

Song Jiang and Ping Zhang

Abstract: We prove the global existence of weak solutions to the Cauchy problem for the compressible isentropic Navier-Stokes equations in ${\Bbb R}^n$ (n=2,3) when the Cauchy data are spherically symmetric. The proof is based on the exploitation of the one-dimensional feature of symmetric solutions and use of a new property induced by the viscous flux. The present paper extends Lions' existence theorem [12] to the case $1<\gamma<\gamma_n$ for spherically symmetric initial data, where $\gamma$ is the specific heat ratio in the pressure, $\gamma_n=3/2$ for n=2 and $\gamma=9/5$ for n=3.

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Author(s):
Song Jiang, <jiang@mail.iapcm.ac.cn>
Ping Zhang, <zp@math03.math.ac.cn>
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