INTERNAL WAVES IN A 2D AQUARIUM

Seminar: 
Analysis
Event time: 
Thursday, February 29, 2024 - 4:00pm
Speaker: 
Zhenhao Li
Speaker affiliation: 
M.I.T
Event description: 

Internal waves describe perturbations of a stable-stratified fluid. In an effectively 2D aquarium ΩR2, internal waves can be modeled by the equation
(2tΔ+2x2)u(x,t)=f(x)cos(λt),t0,xΩ
with Dirichlet boundary and homogeneous initial conditions. The behavior of the equation is intimately related to the underlying classical dynamics, and Dyatlov--Wang--Zworski proved that for Ω 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.