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Research Article | Open Access

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

Yixuan Zhao1, Shuzhen Zhang2( )
School of Mathematics and Big data, Anhui University of Science and Technology, Huainan 232001, China
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China
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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 flowzero dissipation limitcompressible Navier-Stokes equationrarefaction wavevacuum

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Electronic Research Archive
Volume 34 Issue 4,
April 2026
Pages 2157-2177
DOI: 10.3934/era.2026097

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Cite this article:
Zhao Y, Zhang S. 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. https://doi.org/10.3934/era.2026097

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Received: 30 January 2026
Revised: 01 March 2026
Accepted: 05 March 2026
Published: 15 April 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)