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

2018/12/21 by Cao, Yunbai
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.09388

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 C¹ 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,∞ estimate). In particular this improves the recent regularity estimate of such system in weighted W^1,p space for p<6 in [1].

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