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A geometric lower bound on Grad’s number. (English) Zbl 1167.49040
Summary: 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.
MSC:
49Q20 Variational problems in a geometric measure-theoretic setting
49J40 Variational inequalities
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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