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Mathematics of
internal waves in a two-dimensional aquarium
Semyon Dyatlov, Jian Wang and Maciej Zworski |
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Vol. 18 (2025), No. 1, 1–92
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Abstract |
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Following theoretical and experimental work of Maas et al. (Nature 288:6642 (1997), 557–561) 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 (Amer. J. Math. 63 (1941), 141–154) on the Dirichlet problem for hyperbolic equations in two dimensions. |
Keywords
internal wave, attractor, stratified fluid, limiting
absorption
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Mathematical Subject Classification
Primary: 35G16, 76B55
Secondary: 35B40, 76M22
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Milestones
Received: 21 March 2022
Revised: 3 August 2023
Accepted: 11 September 2023
Published: 15 December 2024
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Authors |
| Semyon Dyatlov | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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| Jian Wang | |
| Department of Mathematics University of North Carolina Chapel Hill, NC United States |
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| Maciej Zworski | |
| Department of Mathematics University of California Berkeley, CA United States |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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