[Existence globale pour l'équation de Boltzmann sans troncature]
Nous présentons le premier résultat d'existence globale pour l'équation de Boltzmann sans troncature angulaire, dans le cadre des espaces de Sobolev à poids, dans un cadre proche de l'équilibre, et pour des molécules maxwelliennes. Ces solutions devienent régulières pour tout temps positif. Un point important de la preuve consiste en l'introduction d'une nouvelle norme adaptée à la singularité et aux propriétés de dissipation de l'opérateur de collision linéarisé.
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.
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@article{CRMATH_2010__348_15-16_867_0,
author = {Alexandre, Radjesvarane and Morimoto, Y. and Ukai, S. and Xu, Chao-Jiang and Yang, T.},
title = {Global well-posedness theory for the spatially inhomogeneous {Boltzmann} equation without angular cutoff},
journal = {Comptes Rendus. Math\'ematique},
pages = {867--871},
publisher = {Elsevier},
volume = {348},
number = {15-16},
year = {2010},
doi = {10.1016/j.crma.2010.07.008},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.008/}
}
TY - JOUR AU - Alexandre, Radjesvarane AU - Morimoto, Y. AU - Ukai, S. AU - Xu, Chao-Jiang AU - Yang, T. TI - Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff JO - Comptes Rendus. Mathématique PY - 2010 SP - 867 EP - 871 VL - 348 IS - 15-16 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.008/ DO - 10.1016/j.crma.2010.07.008 LA - en ID - CRMATH_2010__348_15-16_867_0 ER -
%0 Journal Article %A Alexandre, Radjesvarane %A Morimoto, Y. %A Ukai, S. %A Xu, Chao-Jiang %A Yang, T. %T Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff %J Comptes Rendus. Mathématique %D 2010 %P 867-871 %V 348 %N 15-16 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.008/ %R 10.1016/j.crma.2010.07.008 %G en %F CRMATH_2010__348_15-16_867_0
Alexandre, Radjesvarane; Morimoto, Y.; Ukai, S.; Xu, Chao-Jiang; Yang, T. Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff. Comptes Rendus. Mathématique, Tome 348 (2010) no. 15-16, pp. 867-871. doi : 10.1016/j.crma.2010.07.008. http://www.numdam.org/articles/10.1016/j.crma.2010.07.008/
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