Regularity of Stationary Boltzmann Equation in Convex Domains

Regularity of Stationary Solutions to the Linearized Boltzmann Equations

Abstract. We consider the regularity of the solutions to the stationary linearized Boltzmann equations in bounded C convex domains in R for gases with cutoff hard potential and cutoff Maxwellian gases. Suppose that a solution has a bounded weighted L norm in space and velocity with the weight of collision frequency, which is a typical functional space for existence results for boundary value pr...

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

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 prop...

Hydrodynamic Limit of the Stationary Boltzmann Equation in a Slab

We study the stationary solution of the Boltzmann equation in a slab with a constant external force parallel to the boundary and complete accommodation condition on the walls at a specified temperature. We prpve that when the force is sufficiently small there exists a solution which converges, in the hydrodynamic limit, to a local Maxwellian with parameters given by the stationary solution of t...

On the Stationary Boltzmann Equation in R N

Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in ...