Steve Pankavich
Colorado School of Mines

Recent Developments in Collisionless Kinetic Theory: The Vlasov-Maxwell and Vlasov-Poisson Systems

Abstract
In modeling physical phenomena that involve large particle velocities, such as plasmas and high-temperature 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 Vlasov-Maxwell and Vlasov-Poisson 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 well-posedness, asymptotic behavior, and stability of special types of solutions. Finally, a number of interesting open questions will also be included.
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