A Bound from Below on the Temperature for the Navier--Stokes--Fourier System
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...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Society for Industrial and Applied Mathematics
2014
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| Online Access: | http://hdl.handle.net/1721.1/83887 https://orcid.org/0000-0002-8283-8661 |
| Summary: | 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. |
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