On the stability of multi-dimensional rarefaction waves I: the energy estimates

• 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.2025.202.2.2
• 发表日期: 2025-09
• 页码: 631-752
• 关键词: compressible Euler equations; Riemann problem; multi-dimensional rarefaction waves; quasilinear wave equations; compressible euler equations; REMARKABLE NULL STRUCTURES; hyperbolic systems; VORTEX SHEETS; dimensions; EXISTENCE; blowup

摘要

We study the resolution of discontinuous singularities in gas dynamics via rarefaction waves. The mechanism is well-understood in the one-dimensional case. We will prove the nonlinear stability of the Riemann problem for multi-dimensional isentropic Euler equations in the regime of rarefaction waves. The proof relies on the new energy estimates without loss of derivatives. We also give a detailed geometric description of the rarefaction wave fronts. This is the first paper in the series which provides the a priori energy bounds.