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In this paper, we are concerned with the Cauchy problem for isentropic gasdynamics. Through the contribution of many researchers such as Lax, P. D.,Glimm, J., DiPerna, R. J. and Liu, T. P., the decay of solutions wasestablished. They treated with initial data with the small total variation. Onthe other hand, the decay for large initial data has been open for half acentury. Our goal is to provide a new method to analyze this problem. We provethe existence of a global attractor, which yields a decay of solutions forlarge data. To construct approximate solutions, we introduce a modified Godunovscheme.

Decay of solutions of isentropic gas dynamics for large data