Feimin Huang
We study the hyperbolic system of Euler equations for an isothermal, compressible fluid. The 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 establish the Tartar-Murat equalities for both the weak and strong entropies by introducing complex entropies and using the analyitc extension theorem although the strong entropies may not satisfy H^{-1} condition.