[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.
Accepté le :
Publié le :
@article{CRMATH_2009__347_21-22_1237_0,
author = {Alexandre, Radjesvarane and Morimoto, Yoshinori and Ukai, Seiji and Xu, Chao-Jiang and Yang, Tong},
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},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2009.09.015/}
}
TY - JOUR AU - Alexandre, Radjesvarane AU - Morimoto, Yoshinori AU - Ukai, Seiji AU - Xu, Chao-Jiang AU - Yang, Tong 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 UR - http://archive.numdam.org/articles/10.1016/j.crma.2009.09.015/ DO - 10.1016/j.crma.2009.09.015 LA - en ID - CRMATH_2009__347_21-22_1237_0 ER -
%0 Journal Article %A Alexandre, Radjesvarane %A Morimoto, Yoshinori %A Ukai, Seiji %A Xu, Chao-Jiang %A Yang, Tong %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 %U http://archive.numdam.org/articles/10.1016/j.crma.2009.09.015/ %R 10.1016/j.crma.2009.09.015 %G en %F CRMATH_2009__347_21-22_1237_0
Alexandre, Radjesvarane; Morimoto, Yoshinori; Ukai, Seiji; Xu, Chao-Jiang; Yang, Tong. Existence of local solutions for the Boltzmann equation without angular cutoff. Comptes Rendus. Mathématique, Tome 347 (2009) no. 21-22, pp. 1237-1242. doi : 10.1016/j.crma.2009.09.015. http://archive.numdam.org/articles/10.1016/j.crma.2009.09.015/
[1] Some solutions of the Boltzmann equation without angular cutoff, J. Statist. Phys., Volume 104 (2001) no. 1–2, pp. 327-358
[2] Regularity of solutions for the Boltzmann equation without angular cutoff, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009) no. 13–14, pp. 747-752
[3] R. Alexandre, Y. Morimoto, S. Ukai, C.-J. Xu, T. Yang, Regularizing effect and local existence for non-cutoff Boltzmann equation, preprint, 2009, available via | HAL
[4] On the Boltzmann equation for long-range interaction, Comm. Pure Appl. Math., Volume 55 (2002), pp. 30-70
[5] Local solutions in Gevrey classes to the nonlinear Boltzmann equation without cutoff, Japan J. Appl. Math., Volume 1 (1984) no. 1, pp. 141-156
[6] On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Ration. Mech. Anal., Volume 143 (1998), pp. 273-307
[7] A review of mathematical topics in collisional kinetic theory, Handbook of Mathematical Fluid Dynamics, vol. I, North-Holland, Amsterdam, 2002, pp. 71-305
Cité par Sources :
