Sharp Interface Limit for the One-dimensional Compressible Navier-Stokes/Allen-Cahn System with Composite Waves

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Ya-zhou Chen, Yi Peng, Xiao-ding Shi
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引用次数: 0

Abstract

This paper is concerned with the sharp interface limit of Cauchy problem for the one-dimensional compressible Navier-Stokes/Allen-Cahn system with a composite wave consisting of the superposition of a rarefaction wave and a shock wave. Under the assumption that the viscosity coefficient and the reciprocal of mobility coefficient are directly proportional to the interface thickness, we first convert the sharp interface limit of the system into the large time behavior of the composite wave via a natural scaling. Then we prove that the composite wave is asymptotically stable under the small initial perturbations and the small strength of the rarefaction and shock wave. Finally, we show the solution of the Cauchy problem exists for all time, and converges to the composite wave solution of the corresponding Euler equations as the thickness of the interface tends to zero. The proof is mainly based on the energy method and the relative entropy.

具有复合波的一维可压缩纳维-斯托克斯/阿伦-卡恩系统的锐界面极限
本文主要研究一维可压缩 Navier-Stokes/Allen-Cahn 系统中由稀释波和冲击波叠加而成的复合波的尖锐界面极限 Cauchy 问题。在粘滞系数和流动系数倒数与界面厚度成正比的假设下,我们首先通过自然缩放将系统的尖锐界面极限转换为复合波的大时间行为。然后,我们证明复合波在初始扰动较小、稀释波和冲击波强度较小的情况下是渐近稳定的。最后,我们证明了 Cauchy 问题的解在所有时间内都存在,并且随着界面厚度趋于零,收敛于相应欧拉方程的复合波解。证明主要基于能量法和相对熵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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