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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

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00079713/en/
Date
2009
Journal name
Archive for Rational Mechanics and Analysis
Volume
193
Number
2
Publisher
Springer
Pages
227-253
Publication identifier
http://dx.doi.org/10.1007/s00205-009-0233-x
Metadata
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Author(s)
Desvillettes, Laurent
Mouhot, Clément
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 / Keywords
Boltzmann equation; spatially homogeneous; non-cutoff; long-range interactions; hard potentials; soft potentials; moderately soft potentials.

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