Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

Abstract

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.

39 pages, 5 Figures

References in corpus (1)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off

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