A Bound from Below on the Temperature for the Navier--Stokes--Fourier System
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Baer-2013-A BOUND FROM BELOW O.pdf
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244.51 KB
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Author(s)
Baer, Eric
Vasseur, Alexis
Date Issued
July 2013
Journal
SIAM Journal on Mathematical Analysis
Publisher
Society for Industrial and Applied Mathematics
Citation
Baer, Eric, and Alexis Vasseur. “A Bound from Below on the Temperature for the Navier--Stokes--Fourier System.” SIAM Journal on Mathematical Analysis 45, no. 4 (January 2013): 2046-2063. © 2013, Society for Industrial and Applied Mathematics
Version
Final published version
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 [A. Mellet and A. Vasseur, Monatsh. Math., 157 (2009), pp. 143--161], 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∞ bounds of solutions to elliptic equations with bounded measurable coefficients.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1137/120883773
