, Volume 194, Issue 1, pp 253-282
Date: 01 Jul 2009

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

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Abstract

For the spatially homogeneous Boltzmann equation with cutoff hard potentials, it is shown that solutions remain bounded from above uniformly in time by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.

Communicated by Y. Brenier