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Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

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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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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Austin, Austin, TX, 78712, USA

    I. M. Gamba

  2. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    V. Panferov

  3. UMPA, ENS Lyon, 46 allée d’Italie, 69364, Lyon Cedex 07, France

    C. Villani

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  1. I. M. Gamba
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  2. V. Panferov
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  3. C. Villani
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Correspondence to I. M. Gamba.

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Communicated by Y. Brenier

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Gamba, I.M., Panferov, V. & Villani, C. Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation. Arch Rational Mech Anal 194, 253–282 (2009). https://doi.org/10.1007/s00205-009-0250-9

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  • DOI: https://doi.org/10.1007/s00205-009-0250-9

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