论文标题
基于傅立叶的衰变速率锐化速率
Sharpening of decay rates in Fourier based hypocoercivity methods
论文作者
论文摘要
本文基于傅立叶分解和模式估计值处理了两种$ l^2 $低碳化率方法，并在圆环和整个欧几里得空间中的动力学方程式中的收敛速率或衰减率进行了应用。主要思想是通过基于扩散的宏观动力学或基于Lyapunov矩阵不平等的标量产品的更改而获得的扭曲来扰动标准的$ l^2 $规范。我们探讨了涉及福克planck和线性放松操作员的方程式的各种估计。我们在简单的情况下回顾了现有的结果，并关注费率估计的准确性。在一维模型中比较了两种方法。
This paper is dealing with two $L^2$ hypocoercivity methods based on Fourier decomposition and mode-by-mode estimates, with applications to rates of convergence or decay in kinetic equations on the torus and on the whole Euclidean space. The main idea is to perturb the standard $L^2$ norm by a twist obtained either by a nonlocal perturbation build upon diffusive macroscopic dynamics, or by a change of the scalar product based on Lyapunov matrix inequalities. We explore various estimates for equations involving a Fokker-Planck and a linear relaxation operator. We review existing results in simple cases and focus on the accuracy of the estimates of the rates. The two methods are compared in the case of the Goldstein-Taylor model in one-dimension.
