Global strong solutions of the Vlasov-Poisson-Boltzmann system in bounded domains

Abstract

When dilute charged particles are confined in a bounded domain, boundary effects are crucial in the global dynamics. We construct a unique global-in-time solution to the Vlasov-Poisson-Boltzmann system in convex domains with the diffuse boundary condition. The construction is based on an $L^2$-$L^{\infty }$ framework with a novel \textit{nonlinear-normed energy estimate} of a distribution function in weighted $W^{1,p}$-spaces and a $C^{2,\delta }$-estimate of the self-consistent electric potential. Moreover we prove an exponential convergence of the distribution function toward the global Maxwellian.

arXiv commentThe current version of manuscript is published in Archive for Rational Mechanics and Analysis: https://rdcu.be/buOgc

References in corpus (11)

• Decay and Continuity of Boltzmann Equation in Bounded Domains
• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• Regularity of the Boltzmann Equation in Convex Domains
• Asymptotic Stability of the Relativistic Boltzmann Equation for the Soft Potentials
• Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains
• Global Hilbert Expansion for the Vlasov-Poisson-Boltzmann System
• The Boltzmann equation with specular boundary condition in convex domains
• BV-regularity of the Boltzmann equation in Non-Convex Domains
• Global Existence for the Vlasov-Poisson System in Bounded Domains
• Boltzmann Equation with a Large Potential in a Periodic Box
• Decay of the Boltzmann equation with the specular boundary condition in non-convex cylindrical domains

Cited by in corpus (11)

• Global mild solutions of the Landau and non-cutoff Boltzmann equations
• Local Well-posedness of Vlasov-Poisson-Boltzmann Equation with Generalized Diffuse Boundary Condition
• The large amplitude solution of the Boltzmann equation with soft potential
• Low Regularity Solutions for the Vlasov-Poisson-Landau/Boltzmann System
• Global strong solutions to the Vlasov-Poisson-Boltzmann system with soft potential in a bounded domain
• The small Deborah number limit for the fluid-particle flows: incompressible case
• Nonlinear asymptotic stability of inhomogeneous steady solutions to boundary problems of Vlasov-Poisson equation
• Stability of Rarefaction Waves for the Non-cutoff Vlasov-Poisson-Boltzmann System with Physical Boundary
• The Mixed Convex-Concave effect on the regularity of a Boltzmann solution
• Kinetic Models for Semiflexible Polymers in a Half-plane
• On the large amplitude solution of the Boltzmann equation with large external potential and boundary effects