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A free boundary problem for compressible viscous fluids.

In this paper we study a problem which describes the non-stationary motion of a compressible viscous fluid bounded by a free surface. The fluid is supposed to occupy a given bounded domain Ω0 at the initial time f = 0; the initial velocity w0, the initial density ρ0 and the initial temperature 0 are known functions defined in Ω0; finally, the external force field per unit mass 5, the heat supply per unit mass per unit time f and the external pressure p are known functions defined in ]0, Γ0[ χ R.