Singularity of Macroscopic Variables Near Boundary for Gases with Cutoff Hard Potential

Abstract

In this article, the boundary singularity for stationary solutions to the linearized Boltzmann equation with cutoff hard potential is analyzed. A technique using the Holder-type continuity of the integral operator to obtain the integrability of the derivatives of the macroscopic variables is developed. We establish the asymptotic approximation for the gradient of the moments. Our analysis indicates the logarithmic singularity of the gradient of the moments. In particular, our theorem holds for the condensation and evaporation problem.