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 Ω⊂R2Ω⊂R2, internal waves can be modeled by the equation
(∂2tΔ+∂2x2)u(x,t)=f(x)cos(λt),t≥0,x∈Ω(∂t2Δ+∂x22)u(x,t)=f(x)cos(λt),t≥0,x∈Ω
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 ΩΩ 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.