Archive for Rational Mechanics and Analysis

, Volume 194, Issue 1, pp 253–282

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation



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

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

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