Geodesic
Asymptotics of Higher Order Entropies
Vincent Giovangigli1
1CMAP-CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France, vincent.giovangigli@polytechnique.edu
ESAIM. Proceedings, Tome 18 (2007), pp. 99-119

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Higher order entropies are kinetic entropy estimators for fluid models. These quantities are quadratic in the velocity v and temperature T derivatives and have temperature dependent coefficients. We investigate asymptotic expansions of higher order entropies for incompressible flows in terms of the Knudsen and Mach numbers. The correspoding entropic inequalities are obtained when is small enough, provided that the temperature dependence of the thermal conductivity λ and the viscosity η is that given by the kinetic theory. As an example of application of higher order entropic estimates we establish an existence theorem for small Mach number flows.
DOI : 10.1051/proc:071809

Vincent Giovangigli  1

1 CMAP-CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France, vincent.giovangigli@polytechnique.edu 
Vincent Giovangigli. Asymptotics of Higher Order Entropies. ESAIM. Proceedings, Tome 18 (2007), pp. 99-119. doi: 10.1051/proc:071809
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     doi = {10.1051/proc:071809},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc:071809/}
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