Student Harmonic Analysis and PDE Seminar (HADES): Internal waves in stratified fluids and 0th order pseudodifferential operators

Seminar | September 25 | 3:40-5 p.m. | 740 Evans Hall

 Maciej Zworski, UC Berkeley

 Department of Mathematics

Colin de Verdière and Saint-Raymond have recently found a fascinating connection between modeling of internal waves in stratified fluids and spectral theory of 0th order pseudodifferential operators on compact manifolds. The purpose of this talk is to motivate that connection and then explain challenges in spectral theory of 0th order operators, with and without viscosity. Some numerical simulations will illustrate how hyperbolic dynamics of certain classical flows results in concentration of velocities. A sketch of mathematics behind it will then be provided.

The talk is based on a short paper with S Dyatlov which resulted from a "groupe de travail" this winter in Berkeley, with inputs from T de Poyferre and T Laux.