## Kinetic Transport Theory, SS 17## Lecture course (No. 250.079, 2h/week, Vorlesungsverzeichnis) |

Lecturer:Christian Schmeiser

Kinetic transport equations are mathematical descriptions of the dynamics of large particle ensembles in terms of a phase space (i.e. position-velocity space) distribution function. They are sometimes calledmesoscopic models,which places them betweenmicroscopic models,where the dynamics of the individual particles are described, andmacroscopicorcontinuum mechanics models,where the material is described by a finite number of position dependent quantities such as the mass density, the mean velocity, the stress tensor, the temperature etc. Mathematically, kinetic equations typically are integro-differential equations of a particular form. Due to their importance from a modeling point of view, their mathematical theory has become a highly developed subfield of the theory of partial differential equations. The undisputedly most important kinetic equation is theBoltzmann equationfor hard spheres, where the underlying particle system is an idealized 3D-billiard. It is well accepted as a model for ideal gases which, on a macroscopic level, are typically described by theEuleror theNavier-Stokes equations.The latter systems can be formally derived from the Boltzmann equation by procedures calledmacroscopic limits.The main goals of this course are to presentThe presented material is mostly taken from books by C. Cercignani, R. Illner, M. Pulvirenti, and by L. Saint-Raymond.

- a
formal derivationof the Boltzmann equation from the microscopic model,- a proof of a variant of the
DiPerna-Lions theoremon the existence of large global solutions of the Boltzmann equation, and- an introduction to a recent result by
Golse/Saint-Raymondon the convergence of DiPerna-Lions solutions of the Boltzmann equation to so calledLeray solutionsof the incompressible Navier-Stokes equations in a combined macroscopic-small-Mach-number limit.

Schedule:

Mon, 12:30-14:00, seminar room, 8th floor; starting on March 6

News:

- The course is cancelled on March 13 (rector's day), March 27, April 24, June 26
- Lecture notes