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arXiv · 2410.00520

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

Franco Flandoli·Yassine Tahraoui
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Abstract

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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BibTeXRIS

Franco Flandoli, Yassine Tahraoui. 2024-10-01. Stretching of Polymers and turbulence: Fokker Planck equation, special stochastic scaling limit and stationary law. https://arxiv.org/abs/2410.00520

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