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Internal waves in aquariums with characteristic corners

Zhenhao Li
Vol. 7 (2025), No. 2, 445–534
DOI: 10.2140/paa.2025.7.445
Abstract

We give a precise microlocal description of the singular profile that forms in the long-time propagation of internal waves in an effectively two-dimensional aquarium. We allow domains with corners, such as polygons appearing in the experimental setups of Maas, Benielli, Sommeria and Lam (Nature 388:6642 (1997), 557–561). This extends the previous work of Dyatlov, Wang and Zworski (Anal. PDE 18:1 (2025), 1–92), which considered domains with smooth boundary. We show that in addition to singularities that correspond to attractors in the underlying classical dynamics, milder singularities propagate out of the corners as well.

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Keywords
internal waves, b-calculus, limiting absorption principle, propagation estimates
Mathematical Subject Classification
Primary: 35Q35, 35S10, 76B55, 76B70
Milestones
Received: 13 April 2024
Revised: 23 March 2025
Accepted: 3 May 2025
Published: 12 June 2025
Authors
Zhenhao Li
Department of Mathematics
Massachusetts Institute of Technology
Cambridge, MA
United States
© 2025 MSP (Mathematical Sciences Publishers).