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Regularity Theory for the Spatially Homogeneous Boltzmann Equation with Cut-Off

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Abstract.

We develop the regularity theory of the spatially homogeneous Boltzmann equation with cut-off and hard potentials (for instance, hard spheres), by (i) revisiting the Lp theory to obtain constructive bounds, (ii) establishing propagation of smoothness and singularities, (iii) obtaining estimates on the decay of the singularities of the initial datum. Our proofs are based on a detailed study of the “regularity of the gain operator”. An application to the long-time behavior is presented.

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Authors and Affiliations

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

    Clément Mouhot & Cédric Villani

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  1. Clément Mouhot
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  2. Cédric Villani
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Correspondence to Cédric Villani.

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Communicated by Y. Brenier

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Mouhot, C., Villani, C. Regularity Theory for the Spatially Homogeneous Boltzmann Equation with Cut-Off. Arch. Rational Mech. Anal. 173, 169–212 (2004). https://doi.org/10.1007/s00205-004-0316-7

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