Boundary Layer of Boltzmann Equation in 2D Convex Domains

Abstract

Consider the stationary Boltzmann equation in 2D convex domains with diffusive boundary condition. In this paper, we establish the hydrodynamic limits while the boundary layers are present, and derive the steady Navier-Stokes-Fourier system with non-slip boundary conditions. Our contribution focuses on novel weighted $W^{1,\infty }$ estimates for the Milne problem with geometric correction. Also, we develop stronger remainder estimates based on an $L^{2m}-L^{\infty }$ framework.

87 pages

References in corpus (4)

• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation
• Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains
• Asymptotic Analysis of Transport Equation in Annulus