Exponential convergence to equilibrium for the homogeneous Landau equation
Exponential convergence to equilibrium for the homogeneous Landau equation
复制标题
DOI：
10.1016/j.bulsci.2014.12.002
复制
发表时间：
2013-08
期刊：
影响因子：
--
通讯作者：
K. Carrapatoso
中科院分区：
文献类型：
--
作者：
K. Carrapatoso
本文研究了具有硬势的空间齐次朗道方程解的长时间行为。我们证明了一个指数的时间收敛到平衡的最佳速率由相关的线性化运营商的频谱间隙。这一结果改进了Desvillettes和Villani [5]所得到的多项式时间收敛性。我们的方法是基于加权（多项式或拉伸指数）Lp-空间中线性化的朗道算子生成的半群的新的衰减估计，使用Gualdani，Mischler和Mouhot [7]开发的方法。
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].