Radiative Transfer with long-range interactions in the half-space

TL;DR

This paper investigates the mathematical properties of the Radiative Transfer equation in a half-space, establishing regularity results and boundary behavior using averaging lemmas and fractional regularization techniques.

Contribution

It introduces a new averaging lemma for the half-space and demonstrates fractional regularization effects up to the boundary for solutions.

Findings

Established well-posedness and regularity results for the equation.

Proved fractional regularization gain near the boundary.

Developed an averaging lemma specific to the half-space setting.

Abstract

We study the well-posedness and regularity theory for the Radiative Transfer equation in the peaked regime posed in the half-space. An average lemma for the transport equation in the half-space is stablished and used to generate interior regularity for solutions of the model. The averaging also shows a fractional regularization gain up to the boundary for the spatial derivatives.