Mathematics of internal waves in a 2D aquarium
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866910748096069632 |
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| author | Dyatlov, Semyon Wang, Jian Zworski, Maciej |
| author_facet | Dyatlov, Semyon Wang, Jian Zworski, Maciej |
| contents | Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description of singular profiles appearing in long time wave evolution and associate them to classical attractors. That is done by microlocal analysis of the spectral Poincaré problem, leading in particular to a limiting absorption principle. Some aspects of the paper (for instance Section 6) can be considered as a natural microlocal continuation of the work of John on the Dirichlet problem for hyperbolic equations in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_10191 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Mathematics of internal waves in a 2D aquarium Dyatlov, Semyon Wang, Jian Zworski, Maciej Analysis of PDEs Following theoretical and experimental work of Maas et al we consider a linearized model for internal waves in effectively two dimensional aquaria. We provide a precise description of singular profiles appearing in long time wave evolution and associate them to classical attractors. That is done by microlocal analysis of the spectral Poincaré problem, leading in particular to a limiting absorption principle. Some aspects of the paper (for instance Section 6) can be considered as a natural microlocal continuation of the work of John on the Dirichlet problem for hyperbolic equations in two dimensions. |
| title | Mathematics of internal waves in a 2D aquarium |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2112.10191 |