Preprint 2002-008

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 $\R^n$.



Paper:
Available as PostScript (134 Kbytes) or gzipped PostScript (53 Kbytes; uncompress using gunzip).
Author(s):
Song Jiang, <jiang@mail.iapcm.ac.cn>
Ping Zhang, <zp@math03.math.ac.cn>
Publishing information:
Comments:
Submitted by:
<jiang@mail.iapcm.ac.cn> February 5 2002.


[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <conservation@math.ntnu.no>
Last modified: Tue Feb 5 21:14:26 MET 2002