Internal waves in 2D domains with ergodic classical dynamics
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929406536056832 |
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| author | de Verdière, Yves Colin Li, Zhenhao |
| author_facet | de Verdière, Yves Colin Li, Zhenhao |
| contents | We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains bounded. This involves studying the spectrum of a related 0-th order pseudodifferential operator at spectral parameters corresponding to such dynamics. For the special cases of rectangular and elliptic domains, we give an explicit spectral description of that operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13834 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Internal waves in 2D domains with ergodic classical dynamics de Verdière, Yves Colin Li, Zhenhao Analysis of PDEs Mathematical Physics Spectral Theory We study a model of internal waves in an effectively 2D aquarium under periodic forcing. In the case when the underlying classical dynamics has sufficiently irrational rotation number, we prove that the energy of the internal waves remains bounded. This involves studying the spectrum of a related 0-th order pseudodifferential operator at spectral parameters corresponding to such dynamics. For the special cases of rectangular and elliptic domains, we give an explicit spectral description of that operator. |
| title | Internal waves in 2D domains with ergodic classical dynamics |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2306.13834 |