Archive for Rational Mechanics and Analysis

, Volume 194, Issue 1, pp 253–282

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation


DOI: 10.1007/s00205-009-0250-9

Cite this article as:
Gamba, I.M., Panferov, V. & Villani, C. Arch Rational Mech Anal (2009) 194: 253. doi:10.1007/s00205-009-0250-9


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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  3. 3.UMPA, ENS LyonLyon Cedex 07France