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Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules

Authors: Laurent Desvillettes, Giulia Furioli and Elide Terraneo
Journal: Trans. Amer. Math. Soc. 361 (2009), 1731-1747
MSC (2000): Primary 76P05; Secondary 35B65
Published electronically: October 31, 2008
MathSciNet review: 2465814
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Abstract: We prove that Gevrey regularity is propagated by the Boltzmann equation with Maxwellian molecules, with or without angular cut-off. The proof relies on the Wild expansion of the solution to the equation and on the characterization of Gevrey regularity by the Fourier transform.

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Additional Information

Laurent Desvillettes
Affiliation: CMLA, ENS Cachan, CNRS, PRES UniverSud, 61, Avenue du Président Wilson, 94235 Cachan Cedex, France

Giulia Furioli
Affiliation: Dipartimento di Ingegneria dell’Informazione e Metodi Matematici, Università di Bergamo, Viale Marconi 5, I–24044 Dalmine (BG), Italy

Elide Terraneo
Affiliation: Dipartimento di Matematica F. Enriques, Università degli studi di Milano, Via Saldini 50, I–20133 Milano, Italy

Keywords: Homogeneous Boltzmann equation, cut-off and non-cut-off, propagation of regularity, Gevrey class
Received by editor(s): November 20, 2006
Published electronically: October 31, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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