Zero dissipation limit to rarefaction waves with a vacuum for one-dimensional viscous compressible two-phase flows

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Abstract

We are concerned with the zero dissipation limit to rarefaction waves with vacuum for a non-conservative viscous compressible two-fluid system in one dimension. In this paper, given a rarefaction wave with one-side vacuum state, we establish the existence of a solution sequence for the system that approaches this rarefaction wave with vacuum as viscosity vanishes and we derive a uniform convergence rate for this approximation. The result is proved by a scaling argument and an energy method.

Keywords

two-phase flow / zero dissipation limit / compressible Navier-Stokes equation / rarefaction wave / vacuum

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