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

By Franco Flandoli, Dejun Luo. Probability theory and related fields, 2019

139 citations recorded by the source corpus.

The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes equations. As opposed 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.

Subfields: Applied Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/93280e4dbce57d3223b48f83437e855d82aa9ca1

How researchers see this paper

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In Applied Mathematics

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a

In Control and Systems Engineering

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a

In Finance

1. Xiangchan Zhu
2. Rongchan Zhu
3. Martina Hofmanov'a
4. Panagiotis E. Souganidis

Citations in the corpus

• Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier–Stokes equations: Existence and nonuniqueness (2021, background): “A linear multiplicative noise as well as a transport type noise has been shown to prevent blow up of strong solutions in a certain sense with large probability, see Röckner, Zhu and Zhu [RZZ14] and Flandoli, Luo [FL19].”