06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
Mikaela Iacobelli (ETH Zurich) und Toan Nguyen (Penn State University)
14:00 Mikaela Iacobelli (ETH Zurich): Stability and singular limits in plasma physics
15:15 Toan Nguyen (Penn State University): Landau damping in plasma physics
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Mikaela Iacobelli (ETH Zurich): Stability and singular limits in plasma physics
In this colloquium we will present two kinetic models that are used to describe the evolution of charged particles in plasmas: the Vlasov-Poisson system (VP) and the Vlasov-Poisson system with massless electrons (VPME). These systems model respectively the evolution of electrons, and ions in a plasma. We will discuss the well-posedness of these systems, the stability of solutions, and their behaviour under singular limits.
Finally, we will introduce a new class of Wasserstein-type distances specifically designed to tackle stability questions for kinetic equations.
Toan Nguyen (Penn State University): Landau damping in plasma physics
The colloquium is to give a quick overview on the classical notion of Landau damping discovered by Landau in 1946, which will in particular highlight recent mathematical advances on understanding the damping and the large time behavior of a plasma modeled by Vlasov-Poisson and Vlasov-Poisson-Landau systems, including (1) an elementary proof of nonlinear Landau damping for analytic and Gevrey data (joint work with E. Grenier from ENS Lyon and I. Rodnianski from Princeton) and (2) nonlinear Landau damping in the weakly collisional regime for a threshold of initial data with Sobolev regularity (joint work with S. Chaturvedi and J. Luk from Stanford).
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