[Équation de Boltzmann relativiste inhomogène dans l’espace-temps de Robertson–Walker avec des donnés initiales petites]
Dans cet article, nous considérons le problème de Cauchy pour l’équation de Boltzmann relativiste avec des données initiales petites. Nous supposons que la fonction de distribution dépend du temps, de la position et de l’impulsion. Le noyau de collision considéré ici est pour le cas des potentiels durs et l’espace-temps dans lequel l’étude est faite est celui de Robertson–Walker. Nous prouvons un théorème d’existence et d’unicité globale (dans le temps) d’une solution généralisée dans un espace à poids approprié.
In this paper, we consider the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data where the distribution function depends on the time, the position and the impulsion. The collision kernel considered here is for the hard potentials case and the background space-time in which the study is done is the Robertson–Walker space-time. Unique global (in time) mild solution is obtained in a suitable weighted space.
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Keywords: Relativistic Boltzmann equation, Robertson–Walker, inhomogeneous, mild solution
Mot clés : équation de Boltzmann relativiste, Robertson–Walker, inhomogène, solution généralisée
@article{AIF_2017__67_3_947_0,
author = {Takou, \'Etienne and Ciake Ciake, Fid\`ele L.},
title = {Inhomogeneous relativistic {Boltzmann} equation near vacuum in the {Robertson{\textendash}Walker} space-time},
journal = {Annales de l'Institut Fourier},
pages = {947--967},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {67},
number = {3},
year = {2017},
doi = {10.5802/aif.3101},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.3101/}
}
TY - JOUR AU - Takou, Étienne AU - Ciake Ciake, Fidèle L. TI - Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson–Walker space-time JO - Annales de l'Institut Fourier PY - 2017 SP - 947 EP - 967 VL - 67 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3101/ DO - 10.5802/aif.3101 LA - en ID - AIF_2017__67_3_947_0 ER -
%0 Journal Article %A Takou, Étienne %A Ciake Ciake, Fidèle L. %T Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson–Walker space-time %J Annales de l'Institut Fourier %D 2017 %P 947-967 %V 67 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3101/ %R 10.5802/aif.3101 %G en %F AIF_2017__67_3_947_0
Takou, Étienne; Ciake Ciake, Fidèle L. Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson–Walker space-time. Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 947-967. doi : 10.5802/aif.3101. http://archive.numdam.org/articles/10.5802/aif.3101/
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