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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2202.06340 |
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| _version_ | 1866914378745380864 |
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| author | Li, Hai-Liang Wang, Yuexun Xin, Zhouping |
| author_facet | Li, Hai-Liang Wang, Yuexun Xin, Zhouping |
| contents | We establish the local-in-time well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters derived rigorously from incompressible Navier-Stokes system with a moving free surface by Gerbeau-Perthame. Our solutions (the height and velocity) are smooth (the solutions satisfy the equations point-wisely) all the way to the moving boundary, although the height degenerates as a singularity of the distance to the vacuum boundary. The proof is built on some new higher-order weighted energy functional and weighted estimates associated to the degeneracy near the moving vacuum boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_06340 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters Li, Hai-Liang Wang, Yuexun Xin, Zhouping Analysis of PDEs We establish the local-in-time well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters derived rigorously from incompressible Navier-Stokes system with a moving free surface by Gerbeau-Perthame. Our solutions (the height and velocity) are smooth (the solutions satisfy the equations point-wisely) all the way to the moving boundary, although the height degenerates as a singularity of the distance to the vacuum boundary. The proof is built on some new higher-order weighted energy functional and weighted estimates associated to the degeneracy near the moving vacuum boundary. |
| title | Well-posedness of classical solutions to the vacuum free boundary problem of the viscous Saint-Venant system for shallow waters |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2202.06340 |