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

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.

41 pages

References in corpus (3)

• The Vlasov-Poisson-Boltzmann system for the whole range of cutoff soft potentials
• Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition
• The Vlasov-Poisson-Landau System with the Specular-Reflection Boundary Condition