论文标题
2D Navier-Stokes方程的灵敏度分析，并具有连续数据同化的应用
Sensitivity Analysis for the 2D Navier-Stokes Equations with Applications to Continuous Data Assimilation
论文作者
论文摘要
我们严格地证明了正式灵敏度方程相对于与2D不可压缩的Navier-Stokes方程相对的雷诺数。此外，我们通过显示一系列差异商的顺序收敛到2D Navier-Stokes方程和相关数据同化方程的灵敏度方程的唯一解，该方程利用了Azouani，Olson和Titi提出的连续数据同化算法。结果，这种证明方法在差异商方面提供了统一的界限，展示了随着系统不断发展而更改参数的参数恢复算法。我们还注意到，这似乎是对2D Navier-Stokes方程（在零初始数据的自然情况下）的强度或弱解的全球存在和独特性的第一个严格证明，并且可以作为相对于雷诺数数量获得的差异表的限制。
We rigorously prove the well-posedness of the formal sensitivity equations with respect to the Reynolds number corresponding to the 2D incompressible Navier-Stokes equations. Moreover, we do so by showing a sequence of difference quotients converges to the unique solution of the sensitivity equations for both the 2D Navier-Stokes equations and the related data assimilation equations, which utilize the continuous data assimilation algorithm proposed by Azouani, Olson, and Titi. As a result, this method of proof provides uniform bounds on difference quotients, demonstrating parameter recovery algorithms that change parameters as the system evolves will not blow-up. We also note that this appears to be the first such rigorous proof of global existence and uniqueness to strong or weak solutions to the sensitivity equations for the 2D Navier-Stokes equations (in the natural case of zero initial data), and that they can be obtained as a limit of difference quotients with respect to the Reynolds number.
