Steve Pankavich
Colorado School of Mines
Recent Developments in Collisionless Kinetic Theory: The VlasovMaxwell and VlasovPoisson Systems
 Abstract

In modeling physical phenomena that involve large particle velocities, such as plasmas and hightemperature gases, kinetic models are often used to describe the distribution of matter under the influence of particular force fields. Two examples of such models are the VlasovMaxwell and VlasovPoisson systems, which are often used to study plasma dynamics. We will provide a brief overview of the derivation of these PDEs, discuss their (Hamiltonian) structure and properties, and review recent mathematical and physical results concerning wellposedness, asymptotic behavior, and stability of special types of solutions. Finally, a number of interesting open questions will also be included.
