论文标题
部分可观测时空混沌系统的无模型预测
Global existence and optimal decay rate of weak solutions to the co-rotation Hooke dumbbell model
论文作者
论文摘要
在本文中，我们主要研究全球存在和最佳的$ l^2 $衰减率的弱解决方案较弱的hooke哑铃模型。该微麦克罗模型是Navier-Stokes方程与非线性Fokker-Planck方程的耦合。基于缺陷度量传播方法，我们证明了共旋转的胡克哑铃模型接受了一个全局弱解决方案，在不同的集成条件下提供了初始数据。此外，对于通过傅立叶分裂方法获得的弱解决方案，我们获得了$ l^2 $中的最佳时间衰减率。
In this paper, we mainly study global existence and optimal $L^2$ decay rate of weak solutions to the co-rotation Hooke dumbbell model. This micro-macro model is a coupling of the Navier-Stokes equation with a nonlinear Fokker-Planck equation. Based on the defect measure propagation method, we prove that the co-rotation Hooke dumbbell model admits a global weak solution provided the initial data under different integrable conditions. Moreover, we obtain optimal time decay rate in $L^2$ for the weak solutions obtained by the Fourier splitting method.
