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arXiv · 1902.10413

Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary

I. S. Ciuperca·E. Feireisl·M. Jai·A. Petrov
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Abstract

The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant constitutive relations. The equation of state of a real fluid is considered, where the admissible range of density is confined to a bounded interval (hard sphere model). The transport coefficients depend on the temperature in a general way including both gases and liquids behavior. The heart of the paper are new a priori bounds resulting from Trudinger-Moser inequality.

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I. S. Ciuperca, E. Feireisl, M. Jai, A. Petrov. 2019-02-27. Stationary solutions of the Navier-Stokes-Fourier system in planar domains with impermeable boundary. https://arxiv.org/abs/1902.10413

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