Fall 2017, Math 597C:
Topics course on Kinetic Theory
Instructor: Toan T. Nguyen
Time/place: MWF 9:05-9:55am, Boucke 309
Office hours: by appointment
Course Description: I plan to cover, but not limited to, the following topics
· Classical vs. quantum particles
· BBGKY hierarchy from N-particle systems
· Derivation of kinetic models (e.g., Vlasov, Boltzmann equations)
· Collision kernel, Conservation laws, and Boltzmann’s H-theorem
· Hydrodynamics limits
· Homogenous Boltzmann
· Boltzmann near a Maxwellian
· Collision-less models (Vlasov-Poisson / Maxwell)
· Stability theory of a hot plasma
· Slides of my talk in a graduate student seminar.
· See my blog posts for lecture notes.
· C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases. Applied Mathematical Sciences, 1994.
· B. Glassey, The Cauchy problem in kinetic theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996. xii+241 pp.
· A. Bressan, Notes on the Boltzmann equations, Lecture notes for a summer course, SISSA, 2005.
· C. Villani, a review of mathematical topics in collisional kinetic theory, Handbook of mathematical fluid dynamics, Vol. I, North-Holland, Amsterdam, 2002.
· F. Golse, on the dynamics of large particle systems in the mean field limit, Lecture notes in Applied Math and Mechanics book series, 2016.
· C. Cercignani, Boltzmann and its applications, Applied Math Sciences, 1998.