We consider the motion of incompressible viscous fluid in a rectangle, imposing the periodicity condition in one direction and the no-slip boundary condition in the other. Assuming that the flow is subject to an external random force, white in time and regular in space, we construct an estimator for the viscosity using only observations of the enstrophy. The goal of the paper is to prove that the estimator is strongly consistent and asymptotically normal. The proof of consistency is based on the explicit formula for the estimator and some bounds for trajectories, while that of asymptotic normality uses in addition mixing properties of the Navier-Stokes flow.

翻译：我们考虑不可压缩黏性流体在矩形区域内的运动，在一个方向上施加周期性条件，在另一个方向上施加无滑移边界条件。假设流动受到外部随机力的作用，该力在时间上为白噪声，在空间上正则，我们仅利用涡量拟能的观测值构造了一个黏度估计量。本文的目标是证明该估计量具有强相合性与渐近正态性。相合性的证明基于估计量的显式公式以及轨迹的若干界估计，而渐近正态性的证明则额外利用了Navier-Stokes流的混合性质。