Kinetic and related models with applications in the natural sciences

On the wave turbulence theory for stratified flows in the ocean

Minh Binh Tran

University of Wisconsin-Madison

After the pioneering work of Garrett and Munk, the statistics of oceanic internal gravity waves has become a central subject of research in oceanography. The time evolution of the spectral energy of internal waves in the ocean can be described by a near-resonance wave turbulence equation, of quantum Boltzmann type. In this talk, we provide the first rigorous mathematical study for the equation by showing the global existence and uniqueness of strong solutions. This is a joint work with Irene M. Gamba and Leslie M. Smith.