Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition

Abstract

The Vlasov-Poisson-Boltzmann equation is a classical equation governing the dynamics of charged particles with the electric force being self-imposed. We consider the system in a convex domain with the Cercignani-Lampis boundary condition. We construct a uniqueness local-in-time solution based on an $L^{\infty }$-estimate and $W^{1,p}$-estimate. In particular, we develop a new iteration scheme along the characteristic with the Cercignani-Lampis boundary for the $L^{\infty }$-estimate, and an intrinsic decomposition of boundary integral for $W^{1,p}$-estimate.

Chen, H., Kim, C. & Li, Q. Local Well-Posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition. J Stat Phys 179, 535-631 (2020). https://doi.org/10.1007/s10955-020-02545-9