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Zero dissipation limit to rarefaction waves with a vacuum for one-dimensional viscous compressible two-phase flows
Electronic Research Archive 2026, 34(4): 2157-2177
Published: 15 April 2026
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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.

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