no. 1
A blow-up criterion for compressible viscous heat-conductive flows
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 337-350.

Nous étudions un problème de valeur limite initiale pour les équations de Navier–Stokes tridimensionnelles des fluides visqueux conducteurs de chaleur dans un domaine délimité lisse. Nous établissons un critère d'explosion pour les solutions fortes en termes de température et de gradient de vitesse seulement, semblable au critère de Beale–Kato–Majda pour les écoulements incompressibles idéaux.

We study an initial boundary value problem for the three-dimensional Navier–Stokes equations of viscous heat-conductive fluids in a bounded smooth domain. We establish a blow-up criterion for the local strong solutions in terms of the temperature and the gradient of velocity only, similar to the Beale–Kato–Majda criterion for ideal incompressible flows.

DOI : 10.1016/j.anihpc.2009.09.012
Classification : 76N10, 35M10, 35Q30
Mots clés : Blow-up criterion, Strong solutions, Compressible Navier–Stokes equations, Heat-conductive flows 
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     title = {A blow-up criterion for compressible viscous heat-conductive flows},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {337--350},
     publisher = {Elsevier},
     volume = {27},
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Fan, Jishan; Jiang, Song; Ou, Yaobin. A blow-up criterion for compressible viscous heat-conductive flows. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) no. 1, pp. 337-350. doi : 10.1016/j.anihpc.2009.09.012. http://www.numdam.org/articles/10.1016/j.anihpc.2009.09.012/

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