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Relativistic Vlasov-Maxwell-Landau system with the specular reflection boundary condition

PDE and Applied Math Seminar

Speaker: Timur Yastrzhembskiy, Brown University
Location: Zoom
Start time: Thu, Oct 26 2023, 4:10PM

Inspired by fusion in tokamaks, we investigate the initial boundary-value problem for the (special) relativistic Vlasov-Maxwell-Landau (RVML) system with the specular reflection boundary condition (SRBC) in a non-convex domain. It is well known that for the kinetic models, the regularity of a solution is expected to deteriorate significantly near the boundary. The standard energy techniques, which typically rely on differentiating with respect to spatial and velocity variables, become inadequate in such a scenario. Furthermore, the introduction of magnetic effects can trigger singularities even in a half-space domain. This is why the uniqueness of the Vlasov-Maxwell system with the SRBC is unknown, even in the 3D half-space in the absence of external fields. Our main result shows that the RVML with SRBC is well-posed in the near global (relativistic) Maxwellian regime. To the best of our knowledge, this is the first well-posedness result for the system with the Vlasov-Maxwell structure in a 3D bounded domain. The talk is based on a joint work with Hongjie Dong, Yan Guo, and Zhimeng Ouyang.