Regularity theory for the spatially homogeneous Boltzmann equation with cut-off

Details Regularity theory for the spatially homogeneous Boltzmann equation with cut-off Regularity theory for the spatially homogeneous Boltzmann equation with cut-off

2006-07-21

arxiv.org/abs/math/0607539v1

Archive for rational mechanics and analysis 173 (2004) 169-212

Mathematics

Analysis of PDEs

47 pages

Scientific paper

10.1007/s00205-004-0316-7

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.

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