From additive to transport noise in 2D fluid dynamics

Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with additive noise, to transport type noise. The arguments apply bo...

Full description

Saved in:
Bibliographic Details
Published in:Stochastic partial differential equations : analysis and computations 2022-09, Vol.10 (3), p.964-1004
Main Authors: Flandoli, Franco, Pappalettera, Umberto
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Euler-Lagrange equation
Fluid dynamics
Fluid mechanics
Mathematical models
Mathematics
Mathematics and Statistics
Numerical Analysis
Partial Differential Equations
Perturbation
Probability Theory and Stochastic Processes
Statistical Theory and Methods
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Additive noise in Partial Differential equations, in particular those of fluid mechanics, has relatively natural motivations. The aim of this work is showing that suitable multiscale arguments lead rigorously, from a model of fluid with additive noise, to transport type noise. The arguments apply both to small-scale random perturbations of the fluid acting on a large-scale passive scalar and to the action of the former on the large scales of the fluid itself. Our approach consists in studying the (stochastic) characteristics associated to small-scale random perturbations of the fluid, here modelled by stochastic 2D Euler equations with additive noise, and their convergence in the infinite scale separation limit.
ISSN:2194-0401
2194-041X
DOI:10.1007/s40072-022-00249-7