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Internal waves in 2D
domains with ergodic classical dynamics
Yves Colin de Verdière and Zhenhao Li |
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Vol. 5 (2024), No. 3, 735–751
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Abstract |
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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. |
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Keywords
internal waves, ergodic dynamics, Poincaré equation
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Mathematical Subject Classification
Primary: 35A02, 35A09, 35Q35
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Milestones
Received: 4 July 2023
Revised: 21 May 2024
Accepted: 10 June 2024
Published: 30 June 2024
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Authors |
| Yves Colin de Verdière | |
| Université Grenoble Alpes Institut Fourier Saint Martin d’Hères France |
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| Zhenhao Li | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
