Enhanced dissipation for stochastic Navier-Stokes equations with transport noise

Abstract

The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D Navier-Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved for stochastic Navier-Stokes equations in vorticity form; in particular, quantitative estimate allows us to choose the parameters of noise, uniformly in initial vorticity bounded in $L^2$-norm, so that global solutions exist with a large probability sufficiently close to 1.

arXiv commentThe version accepted by J Dyn Diff Equat

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Cited by in corpus (1)

• Finite time mixing and enhanced dissipation for 2D Navier--Stokes equations by Ornstein--Uhlenbeck flow