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Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation

I. M. Gamba·V. Panferov·C. Villani
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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.

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I. M. Gamba, V. Panferov, C. Villani. 2007-01-03. Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation. https://arxiv.org/abs/math/0701081

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