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From correlated to white transport noise in fluid models

De Arnaud Debussche

Apparaît dans la collection : New trends of stochastic nonlinear systems: well-posedeness, dynamics and numerics / Nouvelles tendances en analyse non linéaire stochastique: caractère bien posé, dynamique et aspects numériques

This work investigates variational frameworks for modeling stochastic dynamics in incompressible fluids, focusing on large-scale fluid behavior alongside small-scale stochastic processes. The authors aim to develop a coupled system of equations that captures both scales, using a variational principle formulated with Lagrangians defined on the full flow, and incorporating stochastic transport constraints. The approach smooths the noise term along time, leading to stochastic dynamics as a regularization parameter approaches zero. Initially, fixed noise terms are considered, resulting in a generalized stochastic Euler equation, which becomes problematic as the regularization parameter diminishes. The study then examines connections with existing stochastic frameworks and proposes a new variational principle that couples noise dynamics with large-scale fluid motion. This comprehensive framework provides a stochastic representation of large-scale dynamics while accounting for fine-scale components. Our main result is that the evolution of the small-scale velocity component is governed by a linearized Euler equation with random coefficients, influenced by large-scale transport, stretching, and pressure forcing.

Informations sur la vidéo

Date de captation 20/10/2025
Date de publication 31/10/2025
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs, Doctorants
Réalisateur(s) Luca Recanzone
Format MP4

Données de citation

DOI 10.24350/CIRM.V.20396103
Citer cette vidéo Debussche, Arnaud (20/10/2025). From correlated to white transport noise in fluid models . CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20396103
URL https://dx.doi.org/10.24350/CIRM.V.20396103

Domaine(s)

Physique

Bibliographie

DEBUSSCHE, Arnaud et MÉMIN, Etienne. Variational principles for fully coupled stochastic fluid dynamics across scales. Physica D: Nonlinear Phenomena, 2025, p. 134777. - https://doi.org10.1016/j.physd.2025.134777

Codes MSC

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