Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0701081,
title = {Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation},
author = {I. M. Gamba and V. Panferov and C. Villani},
journal= {arXiv preprint arXiv:math/0701081},
year = {2007}
}