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Publishing Language: Chinese | Open Access

Global existence of weak solutions for three-dimensional compressible Navier-Stokes/Allen-Cahn systems with slip boundary conditions

DongDong CHEN, XinYi FENG, YaZhou CHEN( )
College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China
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Abstract

We have studied the global existence of weak solutions for compressible Navier-Stokes/Allen-Cahn (NSAC) systems with slip boundary conditions, which describe the flow of immiscible two-phase flow with diffusion interfaces. Under the conditions of limited initial energy and adiabatic constant γ > 2, the global existence of weak solutions for initial boundary value problems with Navier-slip boundary conditions is proved using the Faedo-Galerkin approximation and a weak convergence limit.

Keywords

Navier-Stokes/Allen-Cahn systemslip boundary conditionsexistence of weak solution
CLC number: O29

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Journal of Beijing University of Chemical Technology (Natural Science Edition)
Volume 53 Issue 2,
March 2026
Pages 126-133
DOI: 10.13543/j.bhxbzr.2026.02.014

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Cite this article:
CHEN D, FENG X, CHEN Y. Global existence of weak solutions for three-dimensional compressible Navier-Stokes/Allen-Cahn systems with slip boundary conditions. Journal of Beijing University of Chemical Technology (Natural Science Edition), 2026, 53(2): 126-133. https://doi.org/10.13543/j.bhxbzr.2026.02.014

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Received: 07 April 2024
Published: 20 March 2026
© 2026 The Authors.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).