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

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.

44 pages. Accepted by Probab. Theory Related Fields

References in corpus (1)

• Global L_2-solutions of stochastic Navier-Stokes equations

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