Speaker:
Professor Maria Pia Gualdani, George Washington University

Time:
July 20, 22, 2:30-4:30

 

Abstract:

Kinetic equations are used to describe evolution of interacting particles. The most famous kinetic equation is the Boltzmann equation: formulated by Ludwig Boltzmann in 1872, this equation describes motion of a large class of gases. Later, in 1936 Lev Landau derived from the Boltzmann equation a new mathematical model for motion of plasma. This latter equation was named the Landau equation. One of the main features of the Landau and Boltzmann equations is nonlocality meaning that particles interact at large, non-infinitesimal length scales. The Boltzmann and Landau equations present non-local integro-differential operators that are highly nonlinear, singular and with degenerating coefficients. Despite the fact that many mathematicians and physicists have been working on these equations, many important questions are still unanswered due to their mathematical complexity. In this short course we will first give an overview of basic properties of the Landau equation and existing literature and then concentrate on an isotropic model recently introduced by Krieger and Strain and highlight recent results in joint work with N. Guillen.