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

Yixuan Zhao; Shuzhen Zhang; Yixuan Zhao; Shuzhen Zhang

doi:10.3934/era.2026097

Electronic Research Archive

2026, Volume 34, Issue 4: 2157-2177. doi: 10.3934/era.2026097

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Research article

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

Yixuan Zhao ¹,
Shuzhen Zhang ^{2
,
,}

1.
School of Mathematics and Big data, Anhui University of Science and Technology, Huainan 232001, China
2.
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255000, China

Received: 30 January 2026 Revised: 01 March 2026 Accepted: 05 March 2026 Published: 10 March 2026

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.
- two-phase flow,
- zero dissipation limit,
- compressible Navier-Stokes equation,
- rarefaction wave,
- vacuum
Citation: Yixuan Zhao, Shuzhen Zhang. Zero dissipation limit to rarefaction waves with a vacuum for one-dimensional viscous compressible two-phase flows[J]. Electronic Research Archive, 2026, 34(4): 2157-2177. doi: 10.3934/era.2026097

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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.

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