STABILITY OF THE RAREFACTION WAVE IN THE SINGULAR LIMIT OF A SHARP INTERFACE PROBLEM FOR THE COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM

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外文摘要：This paper is concerned with the global well-posedness of the solution to the com-pressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.

外文关键词：

compressible Navier-Stokes equationsAllen-Cahn equationrarefaction wavesharp interface limitstability

作者：

陈云坤、黄彬、施小丁

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作者单位：

School of Mathematics and Computer Science,Anshun University,Anshun 561000,China

College of Mathematics and Physics,Beijing University of Chemical Technology,Beijing 100029,China

基金：

National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaAcademic and Technical Leaders Training Plan of Jiangxi Province

项目编号：

1236104412171024119712171197102020212BCJ23027

出版年：

2024

DOI：

10.1007/s10473-024-0417-3

数学物理学报(英文版)

中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD

影响因子：0.256

ISSN：0252-9602

年,卷(期)：2024.44(4)