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arXiv · 1910.05742

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

Franco Flandoli·Dejun Luo
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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.

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Franco Flandoli, Dejun Luo. 2021-03-11. High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations. https://doi.org/10.1007/s00440-021-01037-5

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