Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914855701708800 |
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| author | Xie, Binqiang Zhao, Bin |
| author_facet | Xie, Binqiang Zhao, Bin |
| contents | In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and $\sqrt{2}$, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler fluids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01938 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids Xie, Binqiang Zhao, Bin Analysis of PDEs 14J60(primary) F.2.2 In this paper, when the magnitude of the Mach number is strictly between some fixed small enough constant and $\sqrt{2}$, we can prove the linear and nonlinear ill-posedness of the Kelvin-Helmholtz problem for compressible ideal fluids. To our best knowledge, this is the first reslult that proves the nonlinear ill-posedness to the Kelvin-Helmholtz problem for the compressible Euler fluids. |
| title | Ill-posedness of the Kelvin-Helmholtz problem for compressible Euler fluids |
| topic | Analysis of PDEs 14J60(primary) F.2.2 |
| url | https://arxiv.org/abs/2407.01938 |