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

2023/02/20 by Tian-Wen Luo, Luo, Tian-Wen, Pin Yu +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2302.09714

openalex publication_date 2023/02/20 · openalex created_date 2023/02/23 · openalex updated_date 2026/07/28

Abstract

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 non-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.

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