Refined wave breaking for the one-dimensional nonlinear shallow water equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917293825458176 |
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| author | Liu, Pingchun Saut, Jean-Claude Sun, Shihan Wang, Yuexun |
| author_facet | Liu, Pingchun Saut, Jean-Claude Sun, Shihan Wang, Yuexun |
| contents | This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography parameters, under a non-cavitation condition which excludes the scenario that the solutions have compact support. We construct smooth initial data with finite $\dot{H}^5$-norm such that the $L^\infty$-norm of the spatial derivative of the solution blows up at one single point in finite time with a precise blowup profile. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Refined wave breaking for the one-dimensional nonlinear shallow water equations Liu, Pingchun Saut, Jean-Claude Sun, Shihan Wang, Yuexun Analysis of PDEs 76B15, 76B03, 35S30, 35A20 This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography parameters, under a non-cavitation condition which excludes the scenario that the solutions have compact support. We construct smooth initial data with finite $\dot{H}^5$-norm such that the $L^\infty$-norm of the spatial derivative of the solution blows up at one single point in finite time with a precise blowup profile. |
| title | Refined wave breaking for the one-dimensional nonlinear shallow water equations |
| topic | Analysis of PDEs 76B15, 76B03, 35S30, 35A20 |
| url | https://arxiv.org/abs/2602.21561 |