On the stability of multi-dimensional rarefaction waves I: the energy estimates
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909319415463936 |
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| author | Luo, Tian-Wen Yu, Pin |
| author_facet | Luo, Tian-Wen Yu, Pin |
| contents | 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 \emph{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 \emph{a priori} energy bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_09714 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the stability of multi-dimensional rarefaction waves I: the energy estimates Luo, Tian-Wen Yu, Pin Analysis of PDEs 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 \emph{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 \emph{a priori} energy bounds. |
| title | On the stability of multi-dimensional rarefaction waves I: the energy estimates |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2302.09714 |