A Cauchy inequality for the Boltzmann equation

The distance to a set of Maxwellians is determined for a family of functions with bounded mass, energy and a small entropy production term. Functions with small masses are close to the null Maxwellian. Functions with masses bounded from below by a constant are approached by functions proportional to the gain term of the Boltzmann operator, taking advantage of its regularity. For these regularizations, the integrands of the entropy production term are small everywhere. Hence classical arguments can be used to obtain the closedness to the set of Maxwellians. Copyright © 2000 John Wiley & Sons, Ltd.