Boundary Singularity of Moments for the Linearized Boltzmann Equation
Journal
Journal of Statistical Physics
Journal Volume
153
Journal Issue
1
Pages
93-118
Date Issued
2013
Author(s)
Abstract
We study the boundary singularity for stationary solutions of the linearized Boltzmann equation with hard-sphere potential. An asymptotic estimate for the gradient of the moments is established, which shows the logarithmic singularity near the boundary. Our formula holds for the solutions of the Milne and Kramers problems obtained by Bardos-Caflish-Nicolaenko (Commun. Pure Appl. Math. 49:323-452, 1986). Our theorem requires the Hölder continuity of the boundary data. In particular, it applies to the complete condensation problem for half space. © 2013 Springer Science+Business Media New York.
Type
journal article