Description
296J Participating Seminar: Applied Mathematics Kinetic Theory
Organizers: Alethea Barbaro and Jacob Bedrossian
Winter 2011
Description
Kinetic theory models the behavior of systems comprised of many small, interacting particles as a distribution in phase space (usually position and velocity). In some sense, this representa- tion lies in the gap between a purely particle description and the hydrodynamic descriptions, such as the Navier-Stokes equations. The canonical kinetic model is the Boltzmann equation for rarefied gas dynamics, for which Boltzmann formulated the famous H-theorem which states that the entropy of a gas tends to increase until equilibrium is reached.
The purpose of this seminar is to familiarize the participants with some physical and mathematical aspects of kinetic theory. The focus of the latter part of the seminar will be the recent work on the decay to equilibrium of the Boltzmann equation due to Desvillettes and Villani [1]. The proof itself is of interest to a wide audience: it closely follows physical intuition and highlights the interplay between the hydrodynamic and dissipative aspects of the Boltzmann equation.
This seminar is meant to be a collaborative learning experience for everyone involved. Regular attendance will be sufficient to receive credit, however, participants are encouraged to present selected parts of the proof and the work on which it depends, developed by Desvillettes, Villani and Toscani over several papers. The pieces presented will be matched approximately with the experience, time availability and interest of the students. Any student interested in the analysis of PDE who is familiar with the material in 266AB, and 245AB is welcome to participate. The seminar will continue into the spring. For questions or more information, contact Alethea Barbaro (alethea@math.ucla.edu) or Jacob Bedrossian (jacob.bedrossian@math.ucla.edu).
References
[1] L. Desvillettes and C. Villani. On the trend to global equillibrium for spatially inhomo- geneous kinetic systems: The Boltzmann equation. Invent. Math., 159:245-316, 2005.
