Vlasov-Maxwell-Boltzmann System

Explore a 47-minute lecture on the Vlasov-Maxwell-Boltzmann (VMB) system delivered by Ning Jiang at the Hausdorff Center for Mathematics. Delve into the two-species VMB system and its scaling, where moments of fluctuations to global Maxwellians converge to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell (NSFM) system with Ohm's law. Learn about the uniform estimates for fluctuations with respect to Knudsen number ε, the establishment of global-in-time classical solutions for VMB, and the rigorous justification of convergence from VMB fluctuations to NSFM classical solutions. Compare this work to Arsenio and Saint-Raymond's breakthrough, which justified the limit from renormalized VMB solutions to dissipative solutions of incompressible viscous electro-magneto-hydrodynamics under corresponding scaling.