论文标题
随机无关leray- $α$带运输噪声的模型：收敛速率和CLT
Stochastic inviscid Leray-$α$ model with transport noise: convergence rates and CLT
论文作者
论文摘要
我们认为由运输噪声驱动的圆环上的随机无关leray- $α$模型。在适当的噪声缩放下，我们证明弱解决方案在某些负Sobolev空间中会融合到确定性粘性Leray- $α$模型的独特解决方案中。这意味着运输噪声将无粘性的leray-$α$模型正常，因此它具有近似弱的唯一性。将这种极限结果解释为大量定律，我们研究了基本的中心极限定理，并提供了明确的收敛速率。
We consider the stochastic inviscid Leray-$α$ model on the torus driven by transport noise. Under a suitable scaling of the noise, we prove that the weak solutions converge, in some negative Sobolev spaces, to the unique solution of the deterministic viscous Leray-$α$ model. This implies that transport noise regularizes the inviscid Leray-$α$ model so that it enjoys approximate weak uniqueness. Interpreting such limit result as a law of large numbers, we study the underlying central limit theorem and provide an explicit convergence rate.
