On the stability of multi-dimensional rarefaction waves II: existence of solutions and applications to Riemann problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909319421755392 |
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| author | Luo, Tian-Wen Yu, Pin |
| author_facet | Luo, Tian-Wen Yu, Pin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_06308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the stability of multi-dimensional rarefaction waves II: existence of solutions and applications to Riemann problem Luo, Tian-Wen Yu, Pin Analysis of PDEs 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. |
| title | On the stability of multi-dimensional rarefaction waves II: existence of solutions and applications to Riemann problem |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.06308 |