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arXiv · 1411.1365

A bound from below on the temperature for the Navier-Stokes-Fourier system

Eric Baer·Alexis Vasseur
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Abstract

We give a uniform bound from below on the temperature for a variant of the compressible Navier-Stokes-Fourier system, under suitable hypotheses. This system of equations forms a mathematical model of the motion of a compressible fluid subject to heat conduction. Building upon the work of [16], we identify a class of weak solutions satisfying a localized form of the entropy inequality (adapted to measure the set where the temperature becomes small) and use a form of the De Giorgi argument for $L^\infty$ bounds of solutions to elliptic equations with bounded measurable coefficients.

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Eric Baer, Alexis Vasseur. 2014-11-05. A bound from below on the temperature for the Navier-Stokes-Fourier system. https://doi.org/10.1137/120883773

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