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

Shuang Hu; Bo Lin; Huini Liu; Zhenning Cai

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arXiv · 2605.19415

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

Shuang Hu·Bo Lin·Huini Liu·Zhenning Cai

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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.

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Shuang Hu, Bo Lin, Huini Liu, Zhenning Cai. 2026-05-19. Global well-posedness of the linearized R13 moment equations with Onsager boundary conditions. https://arxiv.org/abs/2605.19415

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