Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909007556378624 |
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| author | Jang, Juhi Liu, Jiaqi Masmoudi, Nader |
| author_facet | Jang, Juhi Liu, Jiaqi Masmoudi, Nader |
| contents | We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and square-integrable, and which, in finite time, transition to $C^{1-μ}$ regularity for $μ\in [1/2,1)$ near the boundary, leading to the gradient blowup at the boundary. It is based on stability analysis of self-similar waiting time solutions \cite{JLN2025} recently constructed by the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00407 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations Jang, Juhi Liu, Jiaqi Masmoudi, Nader Analysis of PDEs We consider the isentropic compressible Euler equations in the half-line which govern the motion of gaseous fluids in contact with stationary vacuum boundary. We construct a large class of solutions that are initially smooth and square-integrable, and which, in finite time, transition to $C^{1-μ}$ regularity for $μ\in [1/2,1)$ near the boundary, leading to the gradient blowup at the boundary. It is based on stability analysis of self-similar waiting time solutions \cite{JLN2025} recently constructed by the authors. |
| title | Gradient blowup of smooth vacuum solutions to 1D compressible Euler equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.00407 |