Caltech/UCLA/USC Joint Analysis Seminar
UCLA, room MS6221
The Landau equation is one of the cornerstones of kinetic theory. It describes the evolution of a gas of plasma particles. Complementing its physical relevance, the mathematical theory of the Landau equation is very deep, yet incomplete owing to the competing effects of quasilinear diffusion and quadratic growth. Global regularity has eluded researchers because of this competition and a related open question is global uniqueness of weak solutions. This talk introduces the gradient flow structure of the Landau equation to set the foundation for an approach to answering this problem. The construction of the metric which induces the gradient flow structure builds upon the dynamic formulation of classical Wasserstein metrics. This is based on joint work with José A. Carrillo, Matias G. Delgadino, and Laurent Desvillettes.