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arXiv · 2606.13235

Analysis of a nonisothermal Maxwell--Stefan system with degenerate thermal conductivity

Stefanos Georgiadis
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Abstract

We prove the global-in-time existence of weak solutions for the Maxwell--Stefan--Fourier system with physically motivated degenerate thermal conductivity $κ(θ)=θ^α$, for $0<α\leq2$. In contrast to existing nonisothermal compressible theories based on nondegenerate conductivities, the entropy inequality no longer gives control of the quantities $\nablaθ$ and $\nabla \logθ$. The main new ingredient is a renormalized energy estimate, which yields compactness of the temperature and allows the identification of the degenerate heat flux.

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Stefanos Georgiadis. 2026-06-11. Analysis of a nonisothermal Maxwell--Stefan system with degenerate thermal conductivity. https://arxiv.org/abs/2606.13235

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