Regularity for diffuse reflection boundary problem to the stationary linearized Boltzmann equation in a convex domain
Journal
Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Journal Volume
36
Journal Issue
3
Pages
745-782
Date Issued
2019
Abstract
We investigate the regularity issue for the diffuse reflection boundary problem to the stationary linearized Boltzmann equation for hard sphere potential, cutoff hard potential, or cutoff Maxwellian molecular gases in a strictly convex bounded domain. We obtain pointwise estimates for first derivatives of the solution provided the boundary temperature is bounded differentiable and the solution is bounded. This result can be understood as a stationary version of the velocity averaging lemma and mixture lemma. ? 2018 Elsevier Masson SAS
Subjects
Kinetic theory; Linearization; Boundary temperature; Diffuse reflection; Hard-sphere potentials; Linearized Boltzmann equation; Pointwise estimate; regularity; stationary; Strictly convexes; Boltzmann equation
Type
journal article