论文标题
在低纤维化设置中，准序强迫2D随机纳维尔方程的指数混合和限制定理
Exponential mixing and limit theorems of quasi-periodically forced 2D stochastic Navier-Stokes Equations in the hypoelliptic setting
论文作者
论文摘要
我们考虑了由确定性时间准周期力和时间上白色且在傅立叶空间中变性的噪声驱动的圆环上的不可压缩的2D Navier-Stokes方程。我们表明，渐近统计行为的特征是一种准周期不变的度量，该测度指数级吸引所有解决方案的定律。结果对于粘度的任何值$ν> 0 $都是正确的，并且不取决于外部力量的强度。 通过利用这种准周期不变的度量，我们为连续的时间不均匀的解决方案过程建立了强数和中央限制定理的定量版本，并具有明确的收敛速率。事实证明，中心极限定理中的收敛速率取决于准周期性力的准周期频率上通过二磷剂近似特性的时间不均匀性。
We consider the incompressible 2D Navier-Stokes equations on the torus driven by a deterministic time quasi-periodic force and a noise that is white in time and degenerate in Fourier space. We show that the asymptotic statistical behavior is characterized by a quasi-periodic invariant measure that exponentially attracts the law of all solutions. The result is true for any value of the viscosity $ν>0$ and does not depend on the strength of the external forces. By utilizing this quasi-periodic invariant measure, we establish a quantitative version of the strong law of large numbers and central limit theorem for the continuous time inhomogeneous solution processes with explicit convergence rates. It turns out that the convergence rate in the central limit theorem depends on the time inhomogeneity through the Diophantine approximation property on the quasi-periodic frequency of the quasi-periodic force.
