Regularity of Boltzmann equation with external fields in convex domains of diffuse reflection

Abstract

We consider the Boltzmann equation with external fields in strictly convex domains with diffuse reflection boundary condition. As long as the normal derivative of external fields satisfy some sign condition on the boundary (1.8) we construct classical $C^1$ solutions away from the grazing set. As a consequence we construct solutions of Vlasov-Poisson-Boltzmann system having bounded derivatives away from the grazing set (weighted $W^{1,\infty }$ estimate). In particular this improves the recent regularity estimate of such system in weighted $W^{1,p}$ space for $p<6$ in [1].

The author simplified the proof the velocity lemma, and added a few words about it to the introduction

References in corpus (2)

• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• A note on two species collisional plasma in bounded domains

Cited by in corpus (2)

• On Some Recent Progress in the Vlasov-Poisson-Boltzmann System with Diffuse Reflection Boundary
• A note on two species collisional plasma in bounded domains