[Existence locale pour l'équation de Boltzmann sans troncature]
Nous considérons l'équation de Boltzmann inhomogène sans hypothèse de troncature angulaire. Nous montrons l'existence de solutions locales classiques ainsi que leur unicité pour le problème de Cauchy, dans une classe de fonctions exponentiellement décroissantes du type Maxwellian, relativement à la variable de vitesse.
We consider the spatially inhomogeneous Boltzmann equation without angular cutoff. We prove the existence and uniqueness of local classical solutions to the Cauchy problem, in the function space with Maxwellian type exponential decay with respect to the velocity variable.
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@article{CRMATH_2009__347_21-22_1237_0,
author = {Radjesvarane Alexandre and Yoshinori Morimoto and Seiji Ukai and Chao-Jiang Xu and Tong Yang},
title = {Existence of local solutions for the {Boltzmann} equation without angular cutoff},
journal = {Comptes Rendus. Math\'ematique},
pages = {1237--1242},
publisher = {Elsevier},
volume = {347},
number = {21-22},
year = {2009},
doi = {10.1016/j.crma.2009.09.015},
language = {en},
}
TY - JOUR AU - Radjesvarane Alexandre AU - Yoshinori Morimoto AU - Seiji Ukai AU - Chao-Jiang Xu AU - Tong Yang TI - Existence of local solutions for the Boltzmann equation without angular cutoff JO - Comptes Rendus. Mathématique PY - 2009 SP - 1237 EP - 1242 VL - 347 IS - 21-22 PB - Elsevier DO - 10.1016/j.crma.2009.09.015 LA - en ID - CRMATH_2009__347_21-22_1237_0 ER -
%0 Journal Article %A Radjesvarane Alexandre %A Yoshinori Morimoto %A Seiji Ukai %A Chao-Jiang Xu %A Tong Yang %T Existence of local solutions for the Boltzmann equation without angular cutoff %J Comptes Rendus. Mathématique %D 2009 %P 1237-1242 %V 347 %N 21-22 %I Elsevier %R 10.1016/j.crma.2009.09.015 %G en %F CRMATH_2009__347_21-22_1237_0
Radjesvarane Alexandre; Yoshinori Morimoto; Seiji Ukai; Chao-Jiang Xu; Tong Yang. Existence of local solutions for the Boltzmann equation without angular cutoff. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1237-1242. doi : 10.1016/j.crma.2009.09.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.015/
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