Sanchit Chaturvedi (Stanford), Jonathan Luk (Stanford), and I just submitted the paper “The Vlasov–Poisson–Landau system in the weakly collisional regime”, where we prove Landau damping and extra dissipation for plasmas modeled by the physical Vlasov-Poisson-Landau system in the weakly collisional regime , where is the collisional parameter. The results are obtained for Sobolev data that are -close to global Maxwellians on the torus . While Landau damping is a classical subject in plasma physics that predicts mixing and relaxation without dissipation of the electric field in a plasma, extra dissipation arises due to the interplay between phase mixing and entropic relaxation, or between transport and diffusion, which enhances decay to a faster rate than the usual diffusion rate. In this blog post, I give a flavor of the proof of our results, where we develop a purely energy method which combines Guo’s weighted energy method with the hypocoercive energy method and the Klainerman’s vector field method.

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