On the stability of multi-dimensional rarefaction waves II: existence of solutions and applications to the Riemann problem

• 成果类型: Article
• 署名作者: Luo, Tian-Wen; Yu, Pin
• 署名单位: South China Normal University; Tsinghua University
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2025.202.2.3
• 发表日期: 2025-09
• 页码: 753-855
• 关键词: compressible Euler equations; Riemann problem; multi-dimensional rarefaction; waves; quasilinear wave equations; GRAVITATING RELATIVISTIC FLUIDS; FREE PHASE-BOUNDARY; hyperbolic systems; TRANSITION; uniqueness

摘要

This is the second paper in a series studying the nonlinear stability of rarefaction waves in multi-dimensional gas dynamics. We construct initial data near singularities in the rarefaction wave region and, combined with the a priori energy estimates from the first paper, demonstrate that any smooth perturbation of constant states on one side of the diaphragm in a shock tube can be connected to a centered rarefaction wave. We apply this analysis to study multi-dimensional perturbations of the classical Riemann problem for isentropic Euler equations. We show that the Riemann problem is structurally stable in the regime of two families of rarefaction waves.