Fall 2017, Math 597C:

Topics course on Kinetic Theory

 

Course Information:

Instructor: Toan T. Nguyen

Time/place: MWF 9:05-9:55am, Boucke 309

Office hours: by appointment

Syllabus: pdf

 

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

 

Lecture notes:

 

·      Slides of my talk in a graduate student seminar.

·     See my blog posts for lecture notes.

 

Suggested References:

 

·      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.

 

 

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Visit Toan Nguyen's blog: Snapshots in Mathematics!.