Regularity of the Vlasov-Poisson-Boltzmann System without angular cutoff

Abstract

In this paper we study the regularity of the non-cutoff Vlasov-Poisson-Boltzmann system for plasma particles of two species in the whole space ${\mathbb{R}}^3$ with hard potential. The existence of global-in-time nearby Maxwellian solutions is known for soft potential from [15]. However the smoothing effect of these solutions has been a challenging open problem. We establish the global existence and regularizing effect to the Cauchy problem for hard potential with large time decay. Hence, the solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0$. This gives the regularity to Vlasov-Poisson-Boltzmann system, which enjoys a similar smoothing effect as Boltzmann equation. The proof is based on the time-weighted energy method building also upon the pseudo-differential calculus.

References in corpus (13)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Regularizing effect and local existence for non-cutoff Boltzmann equation
• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
• Optimal Large-Time Behavior of the Vlasov-Maxwell-Boltzmann System in the Whole Space
• The Boltzmann equation without angular cutoff in the whole space: III, Qualitative properties of solutions
• Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
• The Vlasov-Poisson-Boltzmann system without angular cutoff
• Optimal time decay of the non cut-off Boltzmann equation in the whole space
• The Vlasov-Poisson-Landau System in ${\mathbb{R}}_x^3$
• Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
• Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
• Regularity of Non-cutoff Boltzmann Equation with Hard Potential

Cited by in corpus (3)

• Global Existence of Non-cutoff Boltzmann Equation in Weighted Sobolev Space
• Stability of Rarefaction Waves for the Non-cutoff Vlasov-Poisson-Boltzmann System with Physical Boundary
• Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential