# Analysis Seminar

#### 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.