### Remarks on Weak Solutions to the Navier-Stokes Equations for 2-D Compressible Isothermal Fluids with Spherically Symmetric Initial Data

Song Jiang and Ping Zhang

Abstract: We prove the existence of global weak solutions to the Cauchy problem for the Navier-Stokes equations of 2-dimensional compressible isothermal fluids when $\rho_0$ and $\mm_0$ are spherically symmetric, $\rho_0\in L^1\cap L_M$ and $\mm_0/\sqrt{\rho_0}\in L^2$, where $\rho_0$ and $\mm_0$ are the initial density and momentum respectively, $L_M$ is the Orlicz space over $\R^2$ with $M=M(s)=(1+s)\ln (1+s)-s$. The proof is based on a compactness lemma which gives a compactness result concerning $H^{n/2}$ and $L_M$ in $\R^n$.

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