Work

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

Year: 2025

Type: article

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.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113789

Authors: Franco Flandoli, Yassine Tahraoui

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: European Commission, European Research Council, HORIZON EUROPE European Research Council

Awards: G1863584654, Noise in Fluids