Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
Mouhot, Clément; Villani, Cédric (2004), Regularity theory for the spatially homogeneous Boltzmann equation with cut-off, Archive for Rational Mechanics and Analysis, 173, 2, p. 169-212. http://dx.doi.org/10.1007/s00205-004-0316-7
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00087274/en/
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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 about the decay of the sin- gularities 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.
Subjects / KeywordsBoltzmann equation ; spatially homogeneous ; hard spheres ; hard potentials ; angular cutoff ; regularity theory ; quantitative ; relaxation to equilibrium
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Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials. Desvillettes, Laurent; Mouhot, Clément (2007) Article accepté pour publication ou publié