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Abstract: The Vlasov-Maxwell-Landau (VML) system and the Vlasov-Maxwell-Boltzmann (VMB) system are fundamental models in dilute collisional plasmas. In this talk, we are concerned with the hydrodynamic limits of both the VML and the non-cutoff VMB systems in the entire space. Our primary objective is to rigorously prove that, within the framework of Hilbert expansion, the unique classical solution of the VML or non-cutoff VMB system converges globally over time to the smooth global solution of the Euler-Maxwell system as the Knudsen number approaches zero.
The core of our analysis hinges on deriving novel interplay energy estimates for the solutions of these two systems, concerning both a local Maxwellian and a global Maxwellian, respectively. Our findings address a problem in the hydrodynamic limit for Landau-type equations and non-cutoff Boltzmann-type equations with a magnetic field. Furthermore, the approach developed can be seamlessly extended to assess the validity of the Hilbert expansion for other types of kinetic equations.
Bio: Huijiang Zhao, professor of School of Mathematics and Statistics of Wuhan University. He got his bachelor degree from Central China Normal University in 1988, and PhD. from the Chinese Academy of Sciences in 1997. He is interested in mathematical theories of nonlinear partial differential equations, especially the global well-posedness of kinetic equations and the corresponding hydrodynamic limits.