Stochastic Navier-Stokes Equations and Related Models

Abstract

Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato [23], is reviewed focusing on 3D Navier-Stokes equations and dyadic models of turbulence.

Effect of random noise on solutions to the modified two-component Camassa-Holm system on $\mathbb{T}^d$

“…For instance, from a stochastic variational principle, Holm [53] derived explicitly some new stochastic fluid equations in the Stratonovich form or Itô form. To just mention a few, we refer to [1,4,13,15,28,29,48,49,69,83,88] for the PDEs theory on some stochastic fluid models, and also refer to recent works on stochastic shallow water wave equations [2,24,27,72,[74][75][76]78,87]. More recently, the compressible fluid flows perturbed by stochastic forcing has been systematically studied by Breit, Feireisl and Hofmanová [8][9][10]12].…”