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

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