Analysis Seminar

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The Vlasov--Poisson--Landau system in the weakly collisional regime

Speaker: Sanchit Chaturvedi, Stanford

Location: Online Online

Date: Thursday, May 6, 2021, 11 a.m.

Synopsis:

Consider the Vlasov-Poisson-Landau system in the weakly collisional regime. We show that solutions near global Maxwellians exhibit enhanced dissipation and Landau damping, resulting in a stronger stability threshold than previously known results. Our result is analogous to an earlier result of Bedrossian for the Vlasov-Poisson-Fokker-Planck system with the same threshold. However, unlike in the Fokker-Planck case, the linear operator cannot be inverted explicitly in the Landau case. For this reason, we develop a strategy based purely on energy methods, which combines Guo's energy method with the hypocoercive energy and the commuting vector field method. Joint work with Jonathan Luk and Toan Nguyen.