Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions
Desvillettes, Laurent; Mouhot, Clément (2009), Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions, Archive for Rational Mechanics and Analysis, 193, 2, p. 227-253. http://dx.doi.org/10.1007/s00205-009-0233-x
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00079713/en/
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)In this paper, we prove some a priori stability estimates (in weighted Sobolev spaces) for the spatially homogeneous Boltzmann equation without angular cutoff (covering every physical collision kernels). These estimates are conditioned to some regularity estimates on the solutions, and therefore reduce the stability and uniqueness issue to the one of proving suitable regularity bounds on the solutions. We then prove such regularity bounds for a class of interactions including the so-called (non cutoff and non mollified) hard potentials and moderately soft potentials. In particular, we obtain the first result of global existence and uniqueness for these long-range interactions.
Subjects / KeywordsBoltzmann equation; spatially homogeneous; non-cutoff; long-range interactions; hard potentials; soft potentials; moderately soft potentials.
Showing items related by title and author.
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