The Steady Relativistic Boltzmann Equation in Half-Space

Abstract

We are concerned with the boundary layer problem for steady relativistic Boltzmann equation in half-space. By introducing some special test functions and choosing suitable estimate orders, we derive a crucial bound on the macroscopic part \(\textbf{P}f\). Under certain admissible conditions and assuming exponential decay for the source term, we demonstrate the existence, continuity and the exponential spacial decay of a boundary layer solution for both linear and nonlinear steady relativistic Boltzmann equations with hard potential collision kernel. The uniqueness is also established under specific constraint conditions.