On the unique solvability of radiative transfer equations with polarization

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.

A metriplectic formulation of polarized radiative transfer

“…with I 2 denoting the 2 × 2 identity matrix. It has been shown that under mild assumptions on v(x), n(x, k) and Σ(x, k) equation ( 15) is well-posed and that the solution W(x, k, t) is Hermitian [9]. Furthermore, the solution is related to the four Stokes parameters I, Q, U, V, see [5,7], as…”