Boundary Singularity for Thermal Transpiration Problem of the Linearized Boltzmann Equation
Journal
Archive for Rational Mechanics and Analysis
Journal Volume
212
Journal Issue
2
Pages
575-595
Date Issued
2014
Author(s)
Abstract
We study the boundary singularity of the fluid velocity for the thermal transpiration problem in the kinetic theory. Logarithmic singularity has been demonstrated through the asymptotic and computational analysis. The goal of this paper is to confirm this logarithmic singularity through exact analysis. We use an iterated scheme, with the "gain" part of the collision operator as a source. The iterated scheme is appropriate for large Knudsen numbers considered here and yields an explicit leading term. © 2014 Springer-Verlag Berlin Heidelberg.
SDGs
Type
journal article