Spring 2015
Colloquia are held on Fridays at 11:30 a.m. in Cullimore Lecture Hall II, unless noted otherwise. Refreshments are served at 11:30 am. For questions about the seminar schedule, please contact Yassine Boubendir.
Date: March 6, 2015
Speaker: Irene Gamba
Department of Mathematics,
University of Texas at Austin
Title: "From Boltzmann Collisional Dynamics to the Landau Equation, Analysis and Numerics"
Abstract:
We discuss the share framework of both the collisional Boltzmann and Landau equations. They are non-local nonlinear statistical flow models of kinetic type whose solutions are probability density functions. These two equations share the feature of preservation of flow invariant quantities, associated to classical conservation laws. As deduced by Landau in 1937, this equation can be approximated by as a grazing collision limit from the Boltzmann model for 'near' Coulombic interactions. We will show, motivated by a spectral representation suitable for an approximation, a priori estimates for the approximation rate of solutions of Boltzmann to solutions of Landau. These rates depend on the choice of angular singularities in the collision kernels. Analysis and numerical methods will be shown. This is work in collaboration with Jeff Haack.