聚合物的拉伸与湍流：Fokker - Planck方程，特殊随机标度极限和平稳定律

IF 2.3 2区数学 Q1 MATHEMATICS

Journal of Differential Equations Pub Date : 2025-09-24 DOI:10.1016/j.jde.2025.113789

Franco Flandoli, Yassine Tahraoui

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引用次数: 0

摘要

这项工作的目的是了解湍流随机模型作用于稀释聚合物的简单模型的拉伸机制。考虑一个时间上为白噪声，激活频率为N≤|k|≤2N的壳层湍流模型，在适当的强度假设下，研究其尺度极限为N→∞，使得拉伸项具有有限的极限协方差。聚合物密度方程，最初是一个SPDE，弱收敛到一个带有新项的极限确定性方程。固定溶液可以计算并显示出聚合物长度的幂律衰减。

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Stretching of polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law

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 2 N

and investigate the scaling limit as

N \to \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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来源期刊

Journal of Differential Equations 数学-数学

CiteScore

4.40

自引率

8.30%

发文量

543

审稿时长

9 months

期刊介绍： The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools. Research Areas Include: • Mathematical control theory • Ordinary differential equations • Partial differential equations • Stochastic differential equations • Topological dynamics • Related topics