基于Van der Waals状态方程的一维可压缩Navier-Stokes/Allen-Cahn方程组稀疏波的渐近稳定性
Asymptotic Stability of Rarefaction Waves for the One-Dimensional Compressible Navier-Stokes/Allen-Cahn Equations Based on the van der Waals Equation of State
摘要: 本文研究了在van der Waals状态方程下，一维可压缩Navier-Stokes/Allen-Cahn方程组Cauchy问题的稀疏波渐近稳定性。在气相区域初值存在小扰动的条件下，通过构造稀疏波的近似解并应用能量估计方法，证明了该稀疏波解的渐近稳定性，且稀疏波强度不需要小性条件。
Abstract: This paper investigates the asymptotic stability of rarefaction wave solutions for the Cauchy problem of the one-dimensional Navier-Stokes/Allen-Cahn equations based on the van der Waals equation of state. Under the condition that the initial data in the gas phase region have small perturbations, the asymptotic stability of the rarefaction wave solutions is proved by constructing approximate solutions of the rarefaction wave and applying the energy method, without requiring the smallness condition on the strength of the rarefaction wave.
文章引用：王泉栋, 廖媛, 彭亿. 基于Van der Waals状态方程的一维可压缩Navier-Stokes/Allen-Cahn方程组稀疏波的渐近稳定性[J]. 理论数学, 2026, 16(6): 102-118. https://doi.org/10.12677/pm.2026.166161

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