Workshop II: The Boltzmann Equation: DiPerna-Lions Plus 20 Years

April 15 - 17, 2009

Overview

Over the last two decades there has been significant progress in the mathematical analysis of kinetic equations, in particular the Boltzmann and Vlasov type particle evolution equations. Areas of discussion of this three-day workshop will include the spatially homogeneous and inhomogeneous Boltzmann equation, their hydrodynamic limits, and collisionless Vlasov models in plasma in the classical and relativistic framework with the coupling to Maxwell-Poisson systems.

For the space homogeneous collisional problem advances have led to a better understanding of regularity and asymptotic behavior. New tools have emerged, including sharp estimates to control very general collision kernels, analysis of high-energy tails and information on asymptotic behavior.

For spatially inhomogeneous scenarios, there has been progress on the initial-boundary value problem for “small-data” perturbations of Maxwellian solutions to the inhomogeneous Boltzmann and corresponding linearized equation, as well as on shock waves, the study of the long time behavior and decay rates of such solutions to Maxwellian equilibria, and on hydrodynamic limits for a wide class of collision kernels. For plasmas and other related models from statistical physics, such as those involving relativistic Einstein Vlasov Maxwell systems, the workshop will focus on issues including existence, stability and long time behavior of solutions.

It is the aim of this workshop to bring together scientists from mathematics, physics, statistical physics, and related disciplines. It will entertain both survey lectures and more technical talks.

Organizing Committee

Irene Gamba, Chair (University of Texas at Austin)
Reinhard Illner (University of Victoria)
David Levermore (University of Maryland, Department of Mathematics)
Laure Saint Raymond (Université de Paris VI (Pierre et Marie Curie))
Marshall Slemrod (University of Wisconsin-Madison, Mathematics)