AMSC 698L Description and Prerequisites

Course Description

AMSC 698L, Mathematics of Kinetic Theory This course is designed to survey current understanding of the justification of fluid dynamics from kinetic theory. After a brief review of classical mechanics, various theories of fluid dynamics will be intorduced from a traditional continuum perspective. The classical Boltzmann equation then will be introduced followed by other kinetic theories. Fluid dynamic regimes will be identified, and various fluid dynamical systems will be derived. Moment closure recipes will be used to derive moment systems for transition regimes. Applications to rarefied gases, semiconductor modeling, radiative transport, and plasmas might be given. A more detailed tentative outline is given below.

Course Prerequisites

This course is intended for both students in mathematics and students in applied fields. Students should have some knowledge of partial differential equations (PDE), either directly or through courses such as fluid mechanics, quantum mechanics, or semiconductor design that use PDE extensively. Some knowledge of classical mechanics or thermodynamics would also be helpful, but is not necessary. Please feel free to contact me concerning your background if you have any questions.

More Details

There will be no exams. Each student will be expected to produce two written reports on somes of the lectures.

Tentative Outline

I. Maxwell-Boltzmann Theory

II. Other Kinetic Theories

III. Fluid Dynamical Approximations

IV. Global Solutions for Fluid Systems

V. Global Solutions for Boltzmann Equations

VI. Global Fluid Limits for Boltzmann Equations