On the unique solvability of radiative transfer equations with polarization

TL;DR

This paper studies the mathematical conditions ensuring the unique solvability of polarized radiative transfer equations with variable refractive index, addressing boundary value problems and properties of solutions.

Contribution

It provides new insights into the well-posedness, trace inequalities, and properties like positivity and Hermiticity of solutions for polarized radiative transfer equations.

Findings

Established conditions for unique solutions

Derived new trace inequalities for matrix products

Analyzed positivity and Hermiticity of solutions

Abstract

We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary value problems on bounded spatial domains, which requires the analysis of suitable trace spaces. Additionally, we discuss positivity, Hermiticity, and norm-preservation of the matrix-valued solution. As auxiliary results, we derive new trace inequalities for products of matrices.