Entropies d'ordre supérieur

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 {norm of matrix} log T {norm of 10.1016/j.crma.2006.06.010matrix}_BMO + {norm of matrix} v / sqrt(T) {norm of matrix}_L ^∞ is small enough, provided that the temperature dependence of the thermal conductivity λ and the viscosity η 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 log (T₀ / T_∞) and v₀ / sqrt(T₀) are small enough in appropriate spaces. To cite this article: V. Giovangigli, C. R. Acad. Sci. Paris, Ser. I 343 (2006).