Singularity of macroscopic variables near boundary for gases with cut-off inverse-power potential

TL;DR

This paper investigates the boundary behavior of solutions to the linearized Boltzmann equation with cut-off inverse power potentials, revealing a logarithmic singularity in the gradient of moments for hard potentials.

Contribution

It provides the first asymptotic approximation for the gradient of moments near the boundary in this context, highlighting the singularity structure.

Findings

Gradient of moments exhibits logarithmic singularity near boundary.

Asymptotic approximation for the gradient of moments in hard-potential cases.

Boundary singularity characterized for stationary solutions of the linearized Boltzmann equation.

Abstract

In this article, the boundary singularity for stationary solutions of the linearized Boltzmann equation with cut-off inverse power potential is analyzed. In particular, for cut-off hard-potential cases, we establish the asymptotic approximation for the gradient of the moments. Our analysis indicates the logarithmic singularity of the gradient of the moments.