### PDE and Differential Geometry SeminarOn L^p solutions to the space homogeneous Landau equation with Coulomb potentialSona Akopian Brown University

Monday, March 25, 2019
2:30pm – 3:30pm

Storrs Campus
MONT 214

The Landau equation models the motion of gas particles in the specific case where there are Coulomb (repulsive) intermolecular forces. This equation was derived heuristically from the Boltzmann equation, heuristically by Landau himself in 1937 and the rigorous mathematical justification came over fifty years later with Degond, Lucquin - Desreux, Desvillettes, Villani and others. For some time, solutions of the Landau equation were studied through the Boltzmann equation before taking the limit to transition into the Landau equation. However, the Boltzmann equation turns out to be very complicated especially in the Coulomb case, and the only global existence theory we have without any extra regularity assumptions is that of very weak solutions (H-solutions) of Villani from 1998. In more recent years, therefore, the Landau equation has been studied directly via techniques for general parabolic equations.

In this talk, we will discuss an abstract but simple family of homogeneous Boltzmann equations for which we can develop an existence theory in $L^p$, and we will see what happens in the limit as the Boltzmann equation transitions into the Landau equation.

Contact:

Wang, lihan.wang@uconn.edu

PDE and Differential Geometry Seminar (primary), UConn Master Calendar