Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff

Radjesvarane Alexandre; Y. Morimoto; S. Ukai; Chao-Jiang Xu; T. Yang

doi:10.1016/j.crma.2010.07.008

Author(s)

Radjesvarane Alexandre
Y. Morimoto
S. Ukai
Chao-Jiang Xu
T. Yang

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	867-871
Journal / Publication	Comptes Rendus Mathematique
Volume	348
Issue number	15-16
Online published	31 Jul 2010
Publication status	Published - Aug 2010

Link(s)

DOI	DOI https://doi.org/10.1016/j.crma.2010.07.008 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-77955768684&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(f25f0015-58a6-41b7-a62f-792842f4e1cb).html

Abstract

We present the first global well-posedness result for the Boltzmann equation without angular cutoff in the framework of weighted Sobolev spaces, in a close to equilibrium framework, and for Maxwellian molecules. These solutions become smooth for any positive time. An important ingredient of the proof rests on the introduction of a new norm, encoding both the singularity and the dissipation properties of the linearized collision operator. © 2010.

Citation Format(s)

[ RIS ] [ BibTeX ]

Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff. / Alexandre, Radjesvarane; Morimoto, Y.; Ukai, S. et al.
In: Comptes Rendus Mathematique, Vol. 348, No. 15-16, 08.2010, p. 867-871.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Alexandre, R, Morimoto, Y, Ukai, S, Xu, C-J & Yang, T 2010, 'Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff', Comptes Rendus Mathematique, vol. 348, no. 15-16, pp. 867-871. https://doi.org/10.1016/j.crma.2010.07.008

Alexandre, R., Morimoto, Y., Ukai, S., Xu, C.-J., & Yang, T. (2010). Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff. Comptes Rendus Mathematique, 348(15-16), 867-871. https://doi.org/10.1016/j.crma.2010.07.008

Alexandre R, Morimoto Y, Ukai S, Xu CJ, Yang T. Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff. Comptes Rendus Mathematique. 2010 Aug;348(15-16):867-871. Epub 2010 Jul 31. doi: 10.1016/j.crma.2010.07.008

Alexandre, Radjesvarane ; Morimoto, Y. ; Ukai, S. et al. / Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff. In: Comptes Rendus Mathematique. 2010 ; Vol. 348, No. 15-16. pp. 867-871.