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Comptes Rendus Mathématique
Volume 343, n° 3
pages 179-184 (août 2006)
Doi : 10.1016/j.crma.2006.06.018
Received : 2 December 2005 ;  accepted : 13 June 2006
Entropies dʼordre supérieur
Higher order entropies
 

Vincent Giovangigli
CMAP-CNRS, École polytechnique, 91128 Palaiseau cedex, France 

Résumé

Les entropies dʼordre supérieur sont des estimateurs dʼentropie cinétique pour les modèles fluides. Ces quantités sont quadratiques en les dérivées de la vitesse v et la température T avec des coefficients dépendants de T . Elles satisfont des inégalités entropiques si   est assez petite, pouvu que la dépendance de la conductivité thermique et de la viscosité en la température soit celle de la théorie cinétique. On obtient dans cette situation de nouvelles estimations a priori des solutions. On établit ensuite un théorème dʼexistence globale lorsque les données initiales   and   sont assez petites dans des espaces appropriés. Pour citer cet article : V. Giovangigli, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Abstract

Higher order entropies are kinetic entropy estimators for fluid models. These quantities are quadratics in the velocity v and temperature T derivatives and have temperature dependent coefficients. We establish entropic inequalities when   is small enough, provided that the temperature dependence of the thermal conductivity and the viscosity is that given by the kinetic theory. In this situation, new a priori estimates for solutions are obtained. We next establish a global existence theorem when the initial values   and   are small enough in appropriate spaces. To cite this article: V. Giovangigli, C. R. Acad. Sci. Paris, Ser. I 343 (2006).

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