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# Jian Wang, UNC-Chapel Hill – Analysis & PDE Seminar

## September 15, 2021 @ 4:00 pm - 5:00 pm

Title: Mathematics of internal waves in a 2D aquarium

Abstract: Internal waves are waves occurring in density stratified fluids. A fascinating feature of internal waves is the appearance of wave attractors in certain shapes of domains in the linear regime (Maas et al, 1997). A microlocal model for the formation of the wave attractors was introduced by Colin de Verdi\`ere — Saint Raymond (2018) by using 0th order psuedodifferential operators over a torus. In the realistic case, where one considers the internal waves in a bounded 2D domain with smooth boundary, the formation of the attractors are connected to the dynamics of homeomorphisms of the circle, and some parts of the study can be regarded as a microlocal continuation of the work the Dirichlet problem for hyperbolic equations by John (1941). In this talk, I will present my results on the spectral aspects of 0th order operators, and then introduce the analysis of internal wave attractors in a 2D aquarium (joint work with Dyatlov and Zworski).