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arXiv · 2111.08946

Global strong solutions to the Vlasov-Poisson-Boltzmann system with soft potential in a bounded domain

Fucai Li·Yichun Wang
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Abstract

Boundary effects are crucial for dynamics of dilute charged gases governed by the Vlasov-Poisson-Boltzmann (VPB) system. In this paper, we study the existence and regularity of solutions to the VPB system with soft potential in a bounded convex domain with in-flow boundary condition. We establish the existence of strong solutions in the time interval $[0,T]$ for an arbitrary given $T>0$ when the initial distribution function is near an absolute Maxwellian. Our contribution is based on a new weighted energy estimate in some $W^{1,p}$ space and $L_x^3 L_v^{1+}$ space for soft potential. By using the classical $L^2$--$L^\infty$ method and bootstrap argument, we extend the local solutions from small time scale to large time scale.

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Fucai Li, Yichun Wang. 2021-11-17. Global strong solutions to the Vlasov-Poisson-Boltzmann system with soft potential in a bounded domain. https://doi.org/10.1016/j.jde.2021.10.023

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