聚合物的拉伸与湍流：Fokker-Planck方程、特殊随机标度极限与平稳律
Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law
AI总结：
本文研究稀聚合物在壳层频率湍流白噪声作用下的拉伸机制，通过取特殊标度极限将SPDE弱收敛到含新项的确定性方程，并求得平稳解呈现聚合物长度的幂律衰减。
摘要：
本工作的目标是理解作用于稀聚合物简单模型上的湍流随机模型的拉伸机制。我们考虑一个在时间上为白噪声、并激活壳层 $N\leq |k|\leq 2N$ 中频率的湍流模型，并在适当强度假设下研究当 $N\rightarrow \infty$ 时的标度极限，使得拉伸项具有有限极限协方差。聚合物密度方程最初是一个SPDE，它弱收敛于一个带有新项的极限确定性方程。可以计算平稳解，并显示其聚合物长度呈幂律衰减。
英文摘要：
The aim of this work is understanding the stretching mechanism of stochastic models of turbulence acting on a simple model of dilute polymers. We consider a turbulent model that is white noise in time and activates frequencies in a shell $N\leq |k|\leq 2N$ and investigate the scaling limit as $N\rightarrow \infty$, under suitable intensity assumption, such that the stretching term has a finite limit covariance. The polymer density equation, initially an SPDE, converges weakly to a limit deterministic equation with a new term. Stationary solutions can be computed and show power law decay in the polymer length.
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