Stability of the composite wave for compressible Navier-Stokes/Allen-Cahn system

被引:16
作者
Luo, Ting [1 ]
Yin, Haiyan [2 ]
Zhu, Changjiang [1 ]
机构
[1] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China
[2] Huagiao Univ, Sch Math Sci, Quanzhou 362021, Peoples R China
基金
中国国家自然科学基金;
关键词
Navier-Stokes/Allen-Cahn system; contact wave; rarefaction wave; composite wave; asymptotic stability; ASYMPTOTIC STABILITY; RAREFACTION WAVES; MODEL; FLUIDS;
D O I
10.1142/S0218202520500098
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper is devoted to the study of the nonlinear stability of the composite wave consisting of two rarefaction waves and a viscous contact wave for the Cauchy problem to a one-dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system which is a combination of the classical Navier-Stokes system with an Allen-Cahn phase field description. We first construct the composite wave through Euler equations under the assumption of chi(x, t) 1 for the large time behavior, and then prove that the composite wave is time asymptotically stable under small perturbations for the corresponding Cauchy problem of the non-isentropic Navier-Stokes/Allen-Cahn system. The proof is mainly based on a basic energy method.
引用
收藏
页码:343 / 385
页数:43
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