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M. Rockner, Ionut́ Munteanu (2016)
The total variation flow perturbed by gradient linear multiplicative noisearXiv: Probability
J. Cooper (1973)
SINGULAR INTEGRALS AND DIFFERENTIABILITY PROPERTIES OF FUNCTIONSBulletin of The London Mathematical Society, 5
N. Jacob (1996)
Pseudo-Differential Operators and Markov Processes
R. Mikulevicius, B. Rozovskii (2004)
Stochastic Navier-Stokes Equations for Turbulent FlowsSIAM J. Math. Anal., 35
A. Bensoussan, R. Temam (1973)
Equations stochastiques du type Navier-StokesJournal of Functional Analysis, 13
A. Calderón, A. Zygmund (1952)
On the existence of certain singular integralsActa Mathematica, 88
R. Mikulevicius, B. Rozovskii (2005)
Global L2-solutions of stochastic Navier–Stokes equationsAnnals of Probability, 33
F. Flandoli, D. Gatarek (1995)
Martingale and stationary solutions for stochastic Navier-Stokes equationsProbability Theory and Related Fields, 102
B. Øksendal (1987)
Stochastic differential equations : an introduction with applicationsJournal of the American Statistical Association, 82
Tosio Kato, H. Fujita (1962)
On the nonstationary Navier-Stokes systemRendiconti del Seminario Matematico della Università di Padova, 32
T Kato, H Fujita (1962)
On the nonstationary Navier–Stokes systemRend. Sem. Mater. Univ. Padova, 32
Z. Brze'zniak, El.zbieta Motyl (2012)
Existence of a martingale solution of the stochastic Navier-Stokes equations in unbounded 2D and 3D-domainsarXiv: Probability
Z. Brzeźniak, M. Capinski, F. Flandoli (1988)
A convergence result for stochastic partial differential equationsStochastics An International Journal of Probability and Stochastic Processes, 24
V. Barbu, M. Rockner (2014)
An operatorial approach to stochastic partial differential equations driven by linear multiplicative noiseJournal of the European Mathematical Society, 17
V. Barbu, M. Röckner (2012)
Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative NoiseArchive for Rational Mechanics and Analysis, 209
R Mikulevicius, BL Rozovskii (2005)
Global $$L^2$$ L 2 -solutions of stochastic Navier–Stokes equationsAnn. Probab., 33
Z. Brzeźniak, M. Capinski, F. Flandoli (1991)
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS AND TURBULENCEMathematical Models and Methods in Applied Sciences, 01
V. Barbu, M. Rockner (2016)
Global solutions to random 3D vorticity equations for small initial dataarXiv: Probability
J. Evol. Equ. Journal of Evolution © 2019 Springer Nature Switzerland AG Equations https://doi.org/10.1007/s00028-019-00551-3 Global solutions for random vorticity equations perturbed by gradient dependent noise, in two and three dimensions Ionut ¸ Munteanu and Michael Röckner Abstract. The aim of this work is to prove an existence and uniqueness result of Kato–Fujita type for the Navier–Stokes equations, in vorticity form, in 2D and 3D, perturbed by a gradient-type multiplicative Gaussian noise (for sufficiently small initial vorticity). These equations are considered in order to model hydrodynamic turbulence. The approach was motivated by a recent result by Barbu and Röckner (J Differ Equ 263:5395–5411, 2017) that treats the stochastic 3D Navier–Stokes equations, in vorticity form, perturbed by linear multiplicative Gaussian noise. More precisely, the equation is transformed to a random nonlinear parabolic equation, as in Barbu and Röckner (2017), but the transformation is different and adapted to our gradient-type noise. Then, global unique existence results are proved for the transformed equation, while for the original stochastic Navier–Stokes equations, existence of a solution adapted to the Brownian filtration is obtained up to some stopping time. 1. Introduction One of the most important features concerning the Navier–Stokes equation is its relation to the
Journal of Evolution Equations – Springer Journals
Published: Nov 9, 2019
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