Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials

被引:24
作者
Carrapatoso, Kleber [1 ]
机构
[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France
来源
BULLETIN DES SCIENCES MATHEMATIQUES | 2015年 / 139卷 / 07期
关键词
Landau equation; Spectral gap; Exponential decay; Hypodissipativity; Hard potentials; LINEARIZED BOLTZMANN; WEAK SOLUTIONS; SPECTRAL GAP; OPERATORS;
D O I
10.1016/j.bulsci.2014.12.002
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This paper deals with the long time behaviour of solutions to the spatially homogeneous Landau equation with hard potentials. We prove an exponential in time convergence towards the equilibrium with the optimal rate given by the spectral gap of the associated linearised operator. This result improves the polynomial in time convergence obtained by Desvillettes and Villani [5]. Our approach is based on new decay estimates for the semigroup generated by the linearised Landau operator in weighted (polynomial or stretched exponential) L-p-spaces, using a method developed by Gualdani, Mischler and Mouhot [7]. (C) 2014 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:777 / 805
页数:29
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