Kinetic Theory

Catalog description

Topics in kinetic theory, particularly concerning Boltzmann equations and related but simpler models (e.g.the Kac model). Key issues include the mathematical derivation of the Boltzmann equation, the Cauchy problem, Boltzmann's $H$ theorem, and hydrodynamic limits yielding the equations of fluid mechanics. We will be most interested in rigorous results, but will not turn away from formal calculations when these are the only things available. A probabilistic viewpoint will be emphasized. In addition to these "traditional'' topics, we will also introduce the Smoluchowski coagulation equation and a similar equation, and some microscopic models described by these in the kinetic limit or exactly. Students should have PDE background equivalent to or exceeding MATH 2370 / APMA 2230 . Familiarity with probability will be helpful, but we will review this according to the audience's needs.