High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations

TL;DR

This paper demonstrates that high mode transport noise can regularize the 3D Navier-Stokes equations, preventing vorticity blow-up and ensuring well-posedness with high probability, especially at high noise intensities.

Contribution

It introduces a novel regularization mechanism using multiplicative transport noise, contrasting previous additive noise approaches with inconclusive results.

Findings

Transport noise provides bounds on vorticity.

High spectrum noise enhances regularization.

Regularization holds with high probability at large noise intensities.

Abstract

The paper is devoted to the open problem of regularization by noise of 3D Navier-Stokes equations. Opposite to several attempts made with additive noise which remained inconclusive, we show here that a suitable multiplicative noise of transport type has a regularizing effect. It is proven that stochastic transport noise provides a bound on vorticity which gives well posedness, with high probability. The result holds for sufficiently large noise intensity and sufficiently high spectrum of the noise.