A geometric lower bound on Grad's number

Issue		ESAIM: COCV Volume 15, Number 3, July-September 2009


Page(s)		569 - 575
DOI		10.1051/cocv:2008032
Published online		26 April 2008

ESAIM: COCV 15 (2009) 569-575
DOI: 10.1051/cocv:2008032

A geometric lower bound on Grad's number

Alessio Figalli

Université de Nice-Sophia Antipolis, Laboratoire J.-A. Dieudonné, UMR 6621, Parc Valrose, 06108 Nice Cedex 02, France; figalli@unice.fr

Received January 13, 2008. Published online April 26, 2008.

Abstract
In this note we provide a new geometric lower bound on the so-called Grad's number of a domain $\Omega$ in terms of how far $\Omega$ is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.

Mathematics Subject Classification. 49Q20, 49J40

Key words: Grad's number, Korn-type inequality, axisymmetry of the domain, trend to equilibrium for the Boltzmann equation

© EDP Sciences, SMAI 2008

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