Global Weak Solutions for 1D Compressible Navier–Stokes/Allen–Cahn System with Vacuum

In this paper, we consider a diffuse interface model coupled by Navier–Stokes equations and Allen–Cahn equations. We study 1D compressible system with free boundary when the initial density is assumed to be compactly supported and connects to vacuum continuously. The global existence of weak solutio...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2023-02, Vol.74 (1), Article 2
Main Authors: Li, Yinghua, Yan, Yuanxiang, Ding, Shijin, Chen, Gaoyang
Format: Article
Language:English
Subjects:
Compressibility
Engineering
Fluid flow
Free boundaries
Mathematical Methods in Physics
Navier-Stokes equations
Theoretical and Applied Mechanics
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Summary:In this paper, we consider a diffuse interface model coupled by Navier–Stokes equations and Allen–Cahn equations. We study 1D compressible system with free boundary when the initial density is assumed to be compactly supported and connects to vacuum continuously. The global existence of weak solutions is established by using line method.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-022-01893-8