论文标题
三维Navier-Stokes方程的连续数据同化
Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations
论文作者
论文摘要
在本文中，我们提供条件，\ emph {仅基于观察到的数据}，以实现Azouni-Olson-TITI数据同化算法（AOT算法）的全球适应性，规律性和收敛性，用于leray-hopf弱解决三层纳维尔 - 纳维尔 - 斯托克斯平等的弱解决方案（3D nse）。观测值的上述条件（在这种情况下，这些条件都包含\ emph {modal}或\ emph {音量元素观测}，对于全球规则且在$ h^1 $ norm中均匀界限的解决方案会自动满足。但是，对于AOT算法的功效，规律性和唯一性都不是必需的。据我们所知，这是对3D NSE的AOT数据同化算法的第一次严格分析。
In this paper, we provide conditions, \emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf weak solutions of the three dimensional Navier-Stokes equations (3D NSE). The aforementioned conditions on the observations, which in this case comprise either of \emph{modal} or \emph{volume element observations}, are automatically satisfied for solutions that are globally regular and are uniformly bounded in the $H^1$-norm. However, neither regularity nor uniqueness is necessary for the efficacy of the AOT algorithm. To the best of our knowledge, this is the first such rigorous analysis of the AOT data assimilation algorithm for the 3D NSE.
