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Journal articles on the topic 'Stochastic Navier-Stokes'

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Published: 4 June 2021
Last updated: 1 February 2022

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1

Bensoussan, A. "Stochastic Navier-Stokes Equations." Acta Applicandae Mathematicae 38, no. 3 (March 1995): 267–304. http://dx.doi.org/10.1007/bf00996149.

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2

Capiński, Marek, and Nigel Cutland. "Stochastic Navier-Stokes equations." Acta Applicandae Mathematicae 25, no. 1 (October 1991): 59–85. http://dx.doi.org/10.1007/bf00047665.

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3

Bela Cruzeiro, Ana. "Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers." Journal of Geometric Mechanics 11, no. 4 (2019): 553–60. http://dx.doi.org/10.3934/jgm.2019027.

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4

Breit, Dominic, and Eduard Feireisl. "Stochastic Navier-Stokes-Fourier equations." Indiana University Mathematics Journal 69, no. 3 (2020): 911–75. http://dx.doi.org/10.1512/iumj.2020.69.7895.

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5

Cruzeiro, Ana Bela. "Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review." Water 12, no. 3 (March 19, 2020): 864. http://dx.doi.org/10.3390/w12030864.

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We present a stochastic Lagrangian view of fluid dynamics. The velocity solving the deterministic Navier–Stokes equation is regarded as a mean time derivative taken over stochastic Lagrangian paths and the equations of motion are critical points of an associated stochastic action functional involving the kinetic energy computed over random paths. Thus the deterministic Navier–Stokes equation is obtained via a variational principle. The pressure can be regarded as a Lagrange multiplier. The approach is based on Itô’s stochastic calculus. Different related probabilistic methods to study the Navier–Stokes equation are discussed. We also consider Navier–Stokes equations perturbed by random terms, which we derive by means of a variational principle.
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6

Shang, Shijie, and Tusheng Zhang. "Approximations of stochastic Navier–Stokes equations." Stochastic Processes and their Applications 130, no. 4 (April 2020): 2407–32. http://dx.doi.org/10.1016/j.spa.2019.07.007.

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7

Zhai, Jianliang, and Tusheng Zhang. "2D stochastic Chemotaxis-Navier-Stokes system." Journal de Mathématiques Pures et Appliquées 138 (June 2020): 307–55. http://dx.doi.org/10.1016/j.matpur.2019.12.009.

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8

Mikulevicius, R., and B. L. Rozovskii. "On unbiased stochastic Navier–Stokes equations." Probability Theory and Related Fields 154, no. 3-4 (August 16, 2011): 787–834. http://dx.doi.org/10.1007/s00440-011-0384-1.

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9

Menaldi, Jose-Luis, and Sivaguru S. Sritharan. "Stochastic 2-D Navier--Stokes Equation." Applied Mathematics and Optimization 46, no. 1 (October 1, 2002): 31–30. http://dx.doi.org/10.1007/s00245-002-0734-6.

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10

Cutland, Nigel J., and Brendan Enright. "Stochastic nonhomogeneous incompressible Navier–Stokes equations." Journal of Differential Equations 228, no. 1 (September 2006): 140–70. http://dx.doi.org/10.1016/j.jde.2006.04.009.

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11

Menaldi, J. L., and S. S. Sritharan. "Impulse control of stochastic Navier–Stokes equations." Nonlinear Analysis: Theory, Methods & Applications 52, no. 2 (January 2003): 357–81. http://dx.doi.org/10.1016/s0362-546x(01)00722-2.

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12

Ferrario, Benedetta. "Ergodic results for stochastic navier-stokes equation." Stochastics and Stochastic Reports 60, no. 3-4 (April 1997): 271–88. http://dx.doi.org/10.1080/17442509708834110.

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13

Brzeźniak, Z., M. Capiński, and F. Flandoli. "Stochastic Navier-stokes equations with multiplicative noise." Stochastic Analysis and Applications 10, no. 5 (January 1992): 523–32. http://dx.doi.org/10.1080/07362999208809288.

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14

Esposito, R., R. Marra, and H. T. Yau. "Navier-Stokes equations for stochastic lattice gases." Physical Review E 53, no. 5 (May 1, 1996): 4486–89. http://dx.doi.org/10.1103/physreve.53.4486.

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15

Bensoussan, Alain, and Jens Frehse. "Local Solutions for Stochastic Navier Stokes Equations." ESAIM: Mathematical Modelling and Numerical Analysis 34, no. 2 (March 2000): 241–73. http://dx.doi.org/10.1051/m2an:2000140.

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16

Mikulevicius, R., and B. L. Rozovskii. "Stochastic Navier--Stokes Equations for Turbulent Flows." SIAM Journal on Mathematical Analysis 35, no. 5 (January 2004): 1250–310. http://dx.doi.org/10.1137/s0036141002409167.

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17

Hofmanova, Martina, and Dominic Breit. "Stochastic Navier-Stokes equations for compressible fluids." Indiana University Mathematics Journal 65, no. 4 (2016): 1183–250. http://dx.doi.org/10.1512/iumj.2016.65.5832.

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18

Arnaudon, Marc, Ana Bela Cruzeiro, and Nuno Galamba. "Lagrangian Navier–Stokes flows: a stochastic model." Journal of Physics A: Mathematical and Theoretical 44, no. 17 (March 30, 2011): 175501. http://dx.doi.org/10.1088/1751-8113/44/17/175501.

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19

Bianchi, Luigi Amedeo, and Franco Flandoli. "Stochastic Navier-Stokes Equations and Related Models." Milan Journal of Mathematics 88, no. 1 (May 12, 2020): 225–46. http://dx.doi.org/10.1007/s00032-020-00312-9.

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20

Mohammed, Salah, and Tusheng Zhang. "Anticipating stochastic 2 D Navier–Stokes equations." Journal of Functional Analysis 264, no. 6 (March 2013): 1380–408. http://dx.doi.org/10.1016/j.jfa.2013.01.002.

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21

Mohammed, Salah, and Tusheng Zhang. "Dynamics of stochastic 2D Navier–Stokes equations." Journal of Functional Analysis 258, no. 10 (May 2010): 3543–91. http://dx.doi.org/10.1016/j.jfa.2009.11.007.

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22

Brzeźniak, Zdzisław, and Gaurav Dhariwal. "Stochastic constrained Navier–Stokes equations on T2." Journal of Differential Equations 285 (June 2021): 128–74. http://dx.doi.org/10.1016/j.jde.2021.02.058.

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23

He, Xinyu. "A probabilistic method for Navier-Stokes vortices." Journal of Applied Probability 38, no. 04 (December 2001): 1059–66. http://dx.doi.org/10.1017/s0021900200019239.

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Consider a Navier-Stokes incompressible turbulent fluid in R 2. Let x(t) denote the position coordinate of a moving vortex with initial circulation Γ0 > 0 in the fluid, subject to a force F. Define x(t) as a stochastic process with continuous sample paths described by a stochastic differential equation. Assuming a suitable notion of weak rotationality, it is shown that the stochastic equation is equivalent to a linear partial differential equation for the complex function ψ, i∂ψ/∂t = [-Γ0Δ + F] ψ, where |ψ|2 = ρ(x,t), ρ being the probability density function of finding the vortex centre in position x at time t.
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24

He, Xinyu. "A probabilistic method for Navier-Stokes vortices." Journal of Applied Probability 38, no. 4 (December 2001): 1059–66. http://dx.doi.org/10.1239/jap/1011994192.

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Consider a Navier-Stokes incompressible turbulent fluid in R2. Let x(t) denote the position coordinate of a moving vortex with initial circulation Γ0 > 0 in the fluid, subject to a force F. Define x(t) as a stochastic process with continuous sample paths described by a stochastic differential equation. Assuming a suitable notion of weak rotationality, it is shown that the stochastic equation is equivalent to a linear partial differential equation for the complex function ψ, i∂ψ/∂t = [-Γ0Δ + F] ψ, where |ψ|2 = ρ(x,t), ρ being the probability density function of finding the vortex centre in position x at time t.
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25

Netzer, Corinna, Michal Pasternak, Lars Seidel, Frédéric Ravet, and Fabian Mauss. "Computationally efficient prediction of cycle-to-cycle variations in spark-ignition engines." International Journal of Engine Research 21, no. 4 (June 13, 2019): 649–63. http://dx.doi.org/10.1177/1468087419856493.

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Cycle-to-cycle variations are important to consider in the development of spark-ignition engines to further increase fuel conversion efficiency. Direct numerical simulation and large eddy simulation can predict the stochastics of flows and therefore cycle-to-cycle variations. However, the computational costs are too high for engineering purposes if detailed chemistry is applied. Detailed chemistry can predict the fuels’ tendency to auto-ignite for different octane ratings as well as locally changing thermodynamic and chemical conditions which is a prerequisite for the analysis of knocking combustion. In this work, the joint use of unsteady Reynolds-averaged Navier–Stokes simulations for the analysis of the average engine cycle and the spark-ignition stochastic reactor model for the analysis of cycle-to-cycle variations is proposed. Thanks to the stochastic approach for the modeling of mixing and heat transfer, the spark-ignition stochastic reactor model can mimic the randomness of turbulent flows that is missing in the Reynolds-averaged Navier–Stokes modeling framework. The capability to predict cycle-to-cycle variations by the spark-ignition stochastic reactor model is extended by imposing two probability density functions. The probability density function for the scalar mixing time constant introduces a variation in the turbulent mixing time that is extracted from the unsteady Reynolds-averaged Navier–Stokes simulations and leads to variations in the overall mixing process. The probability density function for the inflammation time accounts for the delay or advancement of the early flame development. The combination of unsteady Reynolds-averaged Navier–Stokes and spark-ignition stochastic reactor model enables one to predict cycle-to-cycle variations using detailed chemistry in a fraction of computational time needed for a single large eddy simulation cycle.
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26

Marín-Rubio, Pedro, and James C. Robinson. "Attractors for the Stochastic 3D Navier–Stokes Equations." Stochastics and Dynamics 03, no. 03 (September 2003): 279–97. http://dx.doi.org/10.1142/s0219493703000772.

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In a 1997 paper, Ball defined a generalised semiflow as a means to consider the solutions of equations without (or not known to possess) the property of uniqueness. In particular he used this to show that the 3D Navier–Stokes equations have a global attractor provided that all weak solutions are continuous from (0, ∞) into L2. In this paper we adapt his framework to treat stochastic equations: we introduce a notion of a stochastic generalised semiflow, and then show a similar result to Ball's concerning the attractor of the stochastic 3D Navier–Stokes equations with additive white noise.
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27

Peng, Xuhui, and Rangrang Zhang. "Approximations of stochastic 3D tamed Navier-Stokes equations." Communications on Pure & Applied Analysis 19, no. 12 (2020): 5337–65. http://dx.doi.org/10.3934/cpaa.2020241.

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28

Schmalfuss, Björn. "Qualitative properties for the stochastic Navier-Stokes equation." Nonlinear Analysis: Theory, Methods & Applications 28, no. 9 (May 1997): 1545–63. http://dx.doi.org/10.1016/s0362-546x(96)00015-6.

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29

Da Prato, Giuseppe, and Arnaud Debussche. "Ergodicity for the 3D stochastic Navier–Stokes equations." Journal de Mathématiques Pures et Appliquées 82, no. 8 (August 2003): 877–947. http://dx.doi.org/10.1016/s0021-7824(03)00025-4.

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30

Cipriano, Fernanda, and Iván Torrecilla. "Inviscid limit for 2D stochastic Navier–Stokes equations." Stochastic Processes and their Applications 125, no. 6 (June 2015): 2405–26. http://dx.doi.org/10.1016/j.spa.2015.01.005.

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31

Cutland, Nigel J., and Katarzyna Grzesiak. "Optimal control for 3D stochastic Navier–Stokes equations." Stochastics 77, no. 5 (August 2005): 437–54. http://dx.doi.org/10.1080/17442500500236715.

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32

Chueshov, Igor D. "On determining functionals for stochastic navier-stokes equations." Stochastics and Stochastic Reports 68, no. 1-2 (November 1999): 45–64. http://dx.doi.org/10.1080/17442509908834219.

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33

Flandoli, Franco, and Marco Romito. "Partial regularity for the stochastic Navier-Stokes equations." Transactions of the American Mathematical Society 354, no. 6 (February 14, 2002): 2207–41. http://dx.doi.org/10.1090/s0002-9947-02-02975-6.

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34

Blömker, Dirk, Christoph Gugg, and Stanislaus Maier-Paape. "Stochastic Navier–Stokes equation and renormalization group theory." Physica D: Nonlinear Phenomena 173, no. 3-4 (December 2002): 137–52. http://dx.doi.org/10.1016/s0167-2789(02)00621-8.

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35

Mikulevicius, R., and B. L. Rozovskii. "Global L2-solutions of stochastic Navier–Stokes equations." Annals of Probability 33, no. 1 (January 2005): 137–76. http://dx.doi.org/10.1214/009117904000000630.

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36

da Prato, Giuseppe, and Arnaud Debussche. "Dynamic Programming for the stochastic Navier-Stokes equations." ESAIM: Mathematical Modelling and Numerical Analysis 34, no. 2 (March 2000): 459–75. http://dx.doi.org/10.1051/m2an:2000151.

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37

Farrell, Brian F., and Petros J. Ioannou. "Stochastic forcing of the linearized Navier–Stokes equations." Physics of Fluids A: Fluid Dynamics 5, no. 11 (November 1993): 2600–2609. http://dx.doi.org/10.1063/1.858894.

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38

Manna, Utpal, Manil T. Mohan, and Sivaguru S. Sritharan. "Stochastic Navier–Stokes Equations in Unbounded Channel Domains." Journal of Mathematical Fluid Mechanics 17, no. 1 (September 17, 2014): 47–86. http://dx.doi.org/10.1007/s00021-014-0189-y.

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39

Karczewska, Anna. "Foias statistical solution for stochastic Navier — Stokes equation." Nonlinear Analysis: Theory, Methods & Applications 27, no. 1 (July 1996): 97–114. http://dx.doi.org/10.1016/0362-546x(94)00035-g.

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40

Jan, Y. Le, and A. S. Sznitman. "Stochastic cascades and 3-dimensional Navier-Stokes equations." Probability Theory and Related Fields 109, no. 3 (November 4, 1997): 343–66. http://dx.doi.org/10.1007/s004400050135.

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41

Huan, Diem Dang. "Stability of stochastic 2D Navier-Stokes equations with memory and Poisson jumps." Open Journal of Mathematical Sciences 4, no. 1 (November 30, 2020): 417–29. http://dx.doi.org/10.30538/oms2020.0131.

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The objective of this paper is to study the stability of the weak solutions of stochastic 2D Navier-Stokes equations with memory and Poisson jumps. The asymptotic stability of the stochastic Navier-Stoke equation as a semilinear stochastic evolution equation in Hilbert spaces is obtained in both mean square and almost sure senses. Our results can extend and improve some existing ones.
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42

Medjo, Theodore Tachim. "On the existence and uniqueness of solution to a stochastic 2D Allen–Cahn–Navier–Stokes model." Stochastics and Dynamics 19, no. 01 (January 27, 2019): 1950007. http://dx.doi.org/10.1142/s0219493719500072.

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We study, in this paper, a stochastic version of a coupled Allen–Cahn–Navier–Stokes model in a two-dimensional (2D) bounded domain. The model consists of the Navier–Stokes equations (NSEs) for the velocity, coupled with a Allen–Cahn model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.
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43

Li, Shihu, Wei Liu, and Yingchao Xie. "Ergodicity of 3D Leray-α model with fractional dissipation and degenerate stochastic forcing." Infinite Dimensional Analysis, Quantum Probability and Related Topics 22, no. 01 (March 2019): 1950002. http://dx.doi.org/10.1142/s0219025719500024.

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By using the asymptotic coupling method, the asymptotic log-Harnack inequality is established for the transition semigroup associated to the 3D Leray-[Formula: see text] model with fractional dissipation driven by highly degenerate noise. As applications, we derive the asymptotic strong Feller property and ergodicity for the stochastic 3D Leray-[Formula: see text] model with fractional dissipation, which is the stochastic 3D Navier–Stokes equation regularized through a smoothing kernel of order [Formula: see text] in the nonlinear term and a [Formula: see text]-fractional Laplacian. The main results can be applied to the classical stochastic 3D Leray-[Formula: see text] model ([Formula: see text]), stochastic 3D hyperviscous Navier–Stokes equation ([Formula: see text]) and stochastic 3D critical Leray-[Formula: see text] model ([Formula: see text]).
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44

Drivas, Theodore D., and Darryl D. Holm. "Circulation and Energy Theorem Preserving Stochastic Fluids." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 6 (July 23, 2019): 2776–814. http://dx.doi.org/10.1017/prm.2019.43.

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AbstractSmooth solutions of the incompressible Euler equations are characterized by the property that circulation around material loops is conserved. This is the Kelvin theorem. Likewise, smooth solutions of Navier–Stokes are characterized by a generalized Kelvin's theorem, introduced by Constantin–Iyer (2008). In this note, we introduce a class of stochastic fluid equations, whose smooth solutions are characterized by natural extensions of the Kelvin theorems of their deterministic counterparts, which hold along certain noisy flows. These equations are called the stochastic Euler–Poincaré and stochastic Navier–Stokes–Poincaré equations respectively. The stochastic Euler–Poincaré equations were previously derived from a stochastic variational principle by Holm (2015), which we briefly review. Solutions of these equations do not obey pathwise energy conservation/dissipation in general. In contrast, we also discuss a class of stochastic fluid models, solutions of which possess energy theorems but do not, in general, preserve circulation theorems.
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45

Qiu, Jinniao, Shanjian Tang, and Yuncheng You. "2D backward stochastic Navier–Stokes equations with nonlinear forcing." Stochastic Processes and their Applications 122, no. 1 (January 2012): 334–56. http://dx.doi.org/10.1016/j.spa.2011.08.010.

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46

Djurek, Ivan, Danijel Djurek, and Antonio Petošić. "Stochastic solutions of Navier–Stokes equations: An experimental evidence." Chaos: An Interdisciplinary Journal of Nonlinear Science 20, no. 4 (December 2010): 043107. http://dx.doi.org/10.1063/1.3495962.

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47

Bessaih, Hakima, and Benedetta Ferrario. "Inviscid limit of stochastic damped 2D Navier–Stokes equations." Nonlinearity 27, no. 1 (December 16, 2013): 1–15. http://dx.doi.org/10.1088/0951-7715/27/1/1.

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48

Brzeźniak, Zdzisław, Erika Hausenblas, and Jiahui Zhu. "2D stochastic Navier–Stokes equations driven by jump noise." Nonlinear Analysis: Theory, Methods & Applications 79 (March 2013): 122–39. http://dx.doi.org/10.1016/j.na.2012.10.011.

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49

Schmalfuss, B. "Long-Time Behaviour of the Stochastic Navier-Stokes Equation." Mathematische Nachrichten 152, no. 1 (1991): 7–20. http://dx.doi.org/10.1002/mana.19911520102.

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50

Flandoli, Franco. "Irreducibility of the 3-D Stochastic Navier–Stokes Equation." Journal of Functional Analysis 149, no. 1 (September 1997): 160–77. http://dx.doi.org/10.1006/jfan.1996.3089.

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