Archive for Rational Mechanics and Analysis

, Volume 194, Issue 1, pp 253–282

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation


    • Department of MathematicsUniversity of Texas at Austin
  • V. Panferov
    • Department of Mathematics and StatisticsMcMaster University
  • C. Villani
    • UMPA, ENS Lyon

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.

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© Springer-Verlag 2009