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

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 stoc...

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Bibliographic Details
Published inProbability theory and related fields Vol. 180; no. 1-2; pp. 309 - 363
Main Authors Flandoli, Franco, Luo, Dejun
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Economics
Finance
Fluid dynamics
Fluid flow
Insurance
Management
Mathematical analysis
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Navier-Stokes equations
Noise control
Noise intensity
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Regularization
Statistics for Business
Theoretical
Vorticity
Well posedness
Secondary 76D05
Vorticity blow-up control
Primary 60H15
3D Navier–Stokes equations
Transport noise
Regularization by noise
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Summary: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.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-021-01037-5