The Vlasov-Poisson-Landau system in the weakly collisional regime
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 Sanchit Chaturvedi and Toan Nguyen.