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arXiv · 2103.14665

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

Hongxu Chen·Chanwoo Kim·Qin Li
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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.

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Hongxu Chen, Chanwoo Kim, Qin Li. 2021-03-26. Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition. https://doi.org/10.1007/s10955-020-02545-9

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