APMA2210: Topics course:
Boltzmann Equations and Hydrodynamics Limits
Course Information:
Instructor: Toan T. Nguyen
Class meeting time: Tuesdays and Thursdays 9 - 10:20 am
Meeting place: Room 102A, 180G.
Office hours: by appointment
Email: Toan_Nguyen@Brown.edu
Course Description:
So far, I plan to cover the followings: - Formal derivation of Boltzmann (from [1]) - Elementary properties of Boltzmann - Averaging lemmas - Boltzmann near vacuum - Boltzmann near Maxwellian (?) - Various hydrodynamics limits (mostly formal).
Main References:
1. C. Cercignani, R. Illner, and M. Pulvirenti, {\em The Mathematical Theory of Dilute Gases.} Applied Mathematical Sciences.
2. B. Glassey, {\em The Cauchy problem in kinetic theory}, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1996. xii+241 pp.
3. F. Golse and D.C. Levermore, Hydrodynamic limits of kinetic models. {\em Topics in kinetic theory, 1-75, Fields Inst. Commun., 46.}
4. L. Saint-Raymond, {\em Hydrodynamic Limits of the Boltzmann Equation}. Series: Lecture Notes in Mathematics, Vol. 1971