Internal waves in a 2D aquarium

The HADES seminar on Tuesday, October 22th, will be at 2:00pm in Room 740.

Speaker: Zhenhao Li

Abstract: The internal waves equation describes perturbations of a stable-stratified fluid. In an effectively 2D aquarium $\Omega \subset \mathbb{R}^2$, the equation is given by

$ (\partial_t^2 \Delta + \partial_{x_2}^2)u(x, t) = f(x) \cos(\lambda t), \quad t \ge 0, \quad x \in \Omega$

with Dirichlet boundary conditions. The behavior of the equation is intimately related to the underlying classical dynamics, and Dyatlov-Wang-Zworski proved that for $\Omega$ with smooth boundary, strong singularities form along the periodic trajectories of the underlying dynamics. Such phenomenon was first experimentally observed in 1997 by Maas-Lam in an aquarium with corners. We will discuss some recent work proving that corners contribute additional mild singularities that propagate according to the dynamics, matching the experimental observations.

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