## Analysis and Applied Mathematics Seminar

Stanley Snelson

University of Chicago

A priori upper bounds for the inhomogeneous Landau equation

**Abstract:**We consider the Landau equation, an integro-differential kinetic model from plasma physics that describes the evolution of a particle density in phase space. It arises as the limit of the Boltzmann equation when grazing collisions predominate. I will give an overview of prior work on the regularity theory of the Landau equation, and describe how to prove a priori upper bounds that decay polynomially in the velocity variable. The technical tools include precise bounds on the coefficients, and tracking how local estimates scale as the velocity grows. I will also explain why the polynomial decay cannot be improved to exponential decay. This talk is based on joint work with Stephen Cameron and Luis Silvestre.

Monday February 27, 2017 at 4:00 PM in SEO 636