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A maxwellian lower bound for solutions to the Boltzmann equation

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Abstract

We prove that the solution of the spatially homogeneous Boltzmann equation is bounded pointwise from below by a Maxwellian, i.e. a function of the formc 1 exp(-c 2 v 2). This holds for any initial data with bounded mass, energy and entropy, and for any positive timet≧t 0. The constantsc 1, andc 2, depend on the mass, energy and entropy of the initial data, and ont 0>0 only.

A similar result is obtained for the Kac caricature of the Boltzmann equation, where the proof is easier.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pavia, Via Abbiategrasso 215, 27100, Pavia, Italy

    Ada Pulvirenti

  2. Department of Mathematics, Chalmers University of Technology, 41296, Göteborg, Sweden

    Bernt Wennberg

Authors
  1. Ada Pulvirenti
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  2. Bernt Wennberg
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Communicated by J.L. Lebowitz

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Pulvirenti, A., Wennberg, B. A maxwellian lower bound for solutions to the Boltzmann equation. Commun.Math. Phys. 183, 145–160 (1997). https://doi.org/10.1007/BF02509799

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  • DOI: https://doi.org/10.1007/BF02509799

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