Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions

TL;DR

This paper proves the global well-posedness of the linearized R13 moment equations for rarefied gas flows, using entropy inequalities and functional analysis techniques, applicable to Maxwell and non-Maxwell molecules.

Contribution

It establishes the first comprehensive well-posedness results for the linearized R13 equations with Onsager boundary conditions, including steady and time-dependent cases.

Findings

Derived entropy inequality for bounded domains with Onsager boundary conditions.

Proved steady-state well-posedness using LBB theorem and boundary Korn inequalities.

Extended results to time-dependent equations via Lumer-Phillips theorem.

Abstract

This paper establishes the global well-posedness of the linearized regularized 13-moment (R13) equations for rarefied gas flows. We first derive an entropy inequality for the system on bounded domains subject to Onsager boundary conditions. For the steady-state problem, well-posedness is proved via the Ladyzhenskaya-Babuska-Brezzi (LBB) theorem, facilitated by novel boundary-related Korn-type inequalities. Furthermore, leveraging the Lumer-Phillips theorem, we extend these results to guarantee the global well-posedness of the time-dependent R13 equations. Our theoretical framework uniformly accommodates the models for both Maxwell and general non-Maxwell molecules.