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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| 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 |
| _version_ | 1811070388026736640 |
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| author | Baer, Eric Vasseur, Alexis |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Baer, Eric Vasseur, Alexis |
| author_sort | Baer, Eric |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T08:35:10Z |
| format | Article |
| id | mit-1721.1/83887 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:35:10Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | mit-1721.1/838872022-09-23T13:04:03Z A Bound from Below on the Temperature for the Navier--Stokes--Fourier System Baer, Eric Vasseur, Alexis Massachusetts Institute of Technology. Department of Mathematics Baer, Eric 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. National Science Foundation (U.S.) (Award DMS-1204557) 2014-01-13T14:38:05Z 2014-01-13T14:38:05Z 2013-07 2012-07 Article http://purl.org/eprint/type/JournalArticle 0036-1410 1095-7154 http://hdl.handle.net/1721.1/83887 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 https://orcid.org/0000-0002-8283-8661 en_US http://dx.doi.org/10.1137/120883773 SIAM Journal on Mathematical Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics |
| spellingShingle | Baer, Eric Vasseur, Alexis A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title | A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title_full | A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title_fullStr | A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title_full_unstemmed | A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title_short | A Bound from Below on the Temperature for the Navier--Stokes--Fourier System |
| title_sort | bound from below on the temperature for the navier stokes fourier system |
| url | http://hdl.handle.net/1721.1/83887 https://orcid.org/0000-0002-8283-8661 |
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