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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.11508 |
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| _version_ | 1866909350150275072 |
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| author | Li, Qi Saut, Jean-Claude Xu, Li |
| author_facet | Li, Qi Saut, Jean-Claude Xu, Li |
| contents | We prove the existence on long time scales of the solutions to the Cauchy problem for a version of weakly transverse Boussinesq systems arising in the modeling of surface water waves. This system is much more complicated than the isotropic Boussinesq systems because dispersion is only present in the x-direction, leading to anisotropic eigenvalues in the linearized system. This anisotropic character leads to loss of y-derivatives for the solutions. To overcome this main difficulty our strategy is to symmetrize the system by introducing suitable good unknowns in the sense of [3]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11508 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long time existence for a class of weakly transverse Boussinesq systems Li, Qi Saut, Jean-Claude Xu, Li Analysis of PDEs We prove the existence on long time scales of the solutions to the Cauchy problem for a version of weakly transverse Boussinesq systems arising in the modeling of surface water waves. This system is much more complicated than the isotropic Boussinesq systems because dispersion is only present in the x-direction, leading to anisotropic eigenvalues in the linearized system. This anisotropic character leads to loss of y-derivatives for the solutions. To overcome this main difficulty our strategy is to symmetrize the system by introducing suitable good unknowns in the sense of [3]. |
| title | Long time existence for a class of weakly transverse Boussinesq systems |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.11508 |