Abstract:We study the hyperbolic system of Euler equations for an isothermal, compressible fluid. The {\it strong convergence theorem} of approximate solutions is proved by the theory of compensated compactness. The existence of weak entropy solution of Cauchy problems with large $L^\infty$ initial data which may include vacuum is also obtained. We note that we establish the commutation relations not only for the {\it weak} entropies but also for the {\it strong} ones by using the {\it analytic extension theorem}.

**Paper:**- Available as PostScript (264 Kbytes) or gzipped PostScript (112 Kbytes; uncompress using gunzip).
**Author(s):**- Feimin Huang, <fhuang@math.sci.osaka-u.ac.jp>
- Zhen Wang, <mazwang@cityu.edu.hk>
**Publishing information:**- To appear in SIAM J. Math. Anal.
**Comments:****Submitted by:**- <fhuang@math.sci.osaka-u.ac.jp> June 26 2002.

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