BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jose A. Carrillo (University of Oxford) DTSTART:20210107T140000Z DTEND:20210107T145000Z DTSTAMP:20260423T035607Z UID:IMS/72 DESCRIPTION:Title: The Landau equation: Particle Methods & Gradient Flow Structure\nby Jose A. Carrillo (University of Oxford) as part of PDE seminar via Zoom\n\n\nAb stract\nThe Landau equation introduced by Landau in the 1930's is an impor tant partial differential equation in kinetic theory. It gives a descripti on of colliding particles in plasma physics\, and it can be formally deriv ed as a limit of the Boltzmann equation where grazing collisions are domin ant. The purpose of this talk is to propose a new perspective inspired fro m gradient flows for weak solutions of the Landau equation\, which is in a nalogy with the relationship of the heat equation and the 2-Wasserstein me tric gradient flow of the Boltzmann entropy. Moreover\, we aim at using th is interpretation to derive a deterministic particle method to solve effic iently the Landau equation. Our deterministic particle scheme preserves al l the conserved quantities at the semidiscrete level for the regularized L andau equation and that is entropy decreasing. We will illustrate the perf ormance of these schemes with efficient computations using treecode approa ches borrowed from multipole expansion methods for the 3D relevant Coulomb case. From the theoretical viewpoint\, we use the theory of metric measur e spaces for the Landau equation by introducing a bespoke Landau distance $d_L$. Moreover\, we show for a regularized version of the Landau equation that we can construct gradient flow solutions\, curves of maximal slope\, via the corresponding variational scheme. The main result obtained for th e Landau equation shows that the chain rule can be rigorously proved for t he grazing continuity equation\, this implies that H-solutions with certai n apriori estimates on moments and entropy dissipation are equivalent to g radient flow solutions of the Landau equation. We crucially make use of es timates on Fisher information-like quantities in terms of the Landau entro py dissipation developed by Desvillettes.\n LOCATION:https://researchseminars.org/talk/IMS/72/ END:VEVENT END:VCALENDAR