Mathematics – Analysis of PDEs
Scientific paper
2006-07-21
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.
Mouhot Clément
Villani Cedric
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