Abstract:In this paper, we construct a sequence of regular hyperbolic systems (\ref{1.1}) to approximate the general system of isentropic gas dynamics (\ref{1.2}). First, for each fixed approximation parameter $\delta$, we establish the existence of entropy solutions for the Cauchy problem (\ref{1.1}) with bounded initial date (\ref{1.4}). Second, letting $ \E=o(\delta)$, we obtain a simple proof of the $H_{loc}^{-1}$ compactness of weak entropy pairs of system (\ref{1.2}) in the form $ \eta( \rho,u)= \rho H(\rho,u)$ constructed in \cite{CL1,CL2}.

**Paper:**- Available as Postscript (280 Kbytes) or gzipped PostScript (136 Kbytes; uncompress using gunzip).
**Author(s):**- Yunguang Lu, <yglu_2000@yahoo.com>
**Publishing information:****Comments:****Submitted by:**- <yglu_2000@yahoo.com> January 8 2004.

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