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Relevant bibliographies by topics / Stochastic Navier-Stokes

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Academic literature on the topic 'Stochastic Navier-Stokes'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Stochastic Navier-Stokes"

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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Stochastic Navier-Stokes"

1

Li, Yuhong. "Asymptotical behaviour of 2D stochastic Navier-Stokes equations." Thesis, University of Hull, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.411901.

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Osborne, Daniel. "Navier-Stokes equations and stochastic models of turbulence." Thesis, University of Oxford, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.497064.

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Deugoue, Gabriel. "Existence of solutions for stochastic Navier-Stokes alpha and Leray alpha models of fluid turbulence and their relations to the stochastic Navier-Stokes equations." Thesis, University of Pretoria, 2010. http://hdl.handle.net/2263/25566.

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In this thesis, we investigate the stochastic three dimensional Navier-Stokes-∝ model and the stochastic three dimensional Leray-∝ model which arise in the modelling of turbulent flows of fluids. We prove the existence of probabilistic weak solutions for the stochastic three dimensional Navier-Stokes-∝ model. Our model contains nonlinear forcing terms which do not satisfy the Lipschitz conditions. We also discuss the uniqueness. The proof of the existence combines the Galerkin approximation and the compactness method. We also study the asymptotic behavior of weak solutions to the stochastic three dimensional Navier-Stokes-∝ model as ∝ approaches zero in the case of periodic box. Our result provides a new construction of the weak solutions for the stochastic three dimensional Navier-Stokes equations as approximations by sequences of solutions of the stochastic three dimensional Navier-Stokes-∝ model. Finally, we prove the existence and uniqueness of strong solution to the stochastic three dimensional Leray-∝ equations under appropriate conditions on the data. This is achieved by means of the Galerkin approximation combines with the weak convergence methods. We also study the asymptotic behavior of the strong solution as alpha goes to zero. We show that a sequence of strong solution converges in appropriate topologies to weak solutions of the stochastic three dimensional Navier-Stokes equations. All the results in this thesis are new and extend works done by several leading experts in both deterministic and stochastic models of fluid dynamics.
Thesis (PhD)--University of Pretoria, 2010.
Mathematics and Applied Mathematics
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Breckner, Hannelore. "Approximation and optimal control of the stochastic Navier-Stokes equation." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=961407050.

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Enright, Brendan Edward. "A nonstandard approach to the stochastic nonhomogeneous Navier-Stokes equations." Thesis, University of Hull, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322365.

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Carelli, Erich [Verfasser], and Andreas [Akademischer Betreuer] Prohl. "Numerical Analysis of the Stochastic Navier-Stokes equations / Erich Carelli ; Betreuer: Andreas Prohl." Tübingen : Universitätsbibliothek Tübingen, 2012. http://d-nb.info/116284308X/34.

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McKinley, Scott Alister. "An existence result from the theory of fluctuating hydrodynamics of polymers in dilute solution." Columbus, Ohio : Ohio State University, 2006. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1149020682.

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Chen, Bingguang [Verfasser]. "Large and moderate deviation principle for the two-dimensional stochastic Navier-Stokes equations with anisotropic viscosity / Bingguang Chen." Bielefeld : Universitätsbibliothek Bielefeld, 2021. http://d-nb.info/1237048575/34.

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Pranjal, Pranjal. "Optimal iterative solvers for linear systems with stochastic PDE origins : balanced black-box stopping tests." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/optimal-iterative-solvers-for-linear-systems-with-stochastic-pde-origins-balanced-blackbox-stopping-tests(4fd0d668-3271-4615-9def-07fc9fe2ea9e).html.

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The central theme of this thesis is the design of optimal balanced black-box stopping criteria in iterative solvers of symmetric positive-definite, symmetric indefinite, and nonsymmetric linear systems arising from finite element approximation of stochastic (parametric) partial differential equations. For a given stochastic and spatial approximation, it is known that iteratively solving the corresponding linear(ized) system(s) of equations to too tight algebraic error tolerance results in a wastage of computational resources without decreasing the usually unknown approximation error. In order to stop optimally-by avoiding unnecessary computations and premature stopping-algebraic error and a posteriori approximation error estimate must be balanced at the optimal stopping iteration. Efficient and reliable a posteriori error estimators do exist for close estimation of the approximation error in a finite element setting. But the algebraic error is generally unknown since the exact algebraic solution is not usually available. Obtaining tractable upper and lower bounds on the algebraic error in terms of a readily computable and monotonically decreasing quantity (if any) of the chosen iterative solver is the distinctive feature of the designed optimal balanced stopping strategy. Moreover, this work states the exact constants, that is, there are no user-defined parameters in the optimal balanced stopping tests. Hence, an iterative solver incorporating the optimal balanced stopping methodology that is presented here will be a black-box iterative solver. Typically, employing such a stopping methodology would lead to huge computational savings and in any case would definitely rule out premature stopping. The constants in the devised optimal balanced black-box stopping tests in MINRES solver for solving symmetric positive-definite and symmetric indefinite linear systems can be estimated cheaply on-the- fly. The contribution of this thesis goes one step further for the nonsymmetric case in the sense that it not only provides an optimal balanced black-box stopping test in a memory-expensive Krylov solver like GMRES but it also presents an optimal balanced black-box stopping test in memory-inexpensive Krylov solvers such as BICGSTAB(L), TFQMR etc. Currently, little convergence theory exists for the memory-inexpensive Krylov solvers and hence devising stopping criteria for them is an active field of research. Also, an optimal balanced black-box stopping criterion is proposed for nonlinear (Picard or Newton) iterative method that is used for solving the finite dimensional Navier-Stokes equations. The optimal balanced black-box stopping methodology presented in this thesis can be generalized for any iterative solver of a linear(ized) system arising from numerical approximation of a partial differential equation. The only prerequisites for this purpose are the existence of a cheap and tight a posteriori error estimator for the approximation error along with cheap and tractable bounds on the algebraic error.

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Connell, R. J. "Unstable equilibrium : modelling waves and turbulence in water flow." Diss., Lincoln University, 2008. http://hdl.handle.net/10182/592.

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This thesis develops a one-dimensional version of a new data driven model of turbulence that uses the KL expansion to provide a spectral solution of the turbulent flow field based on analysis of Particle Image Velocimetry (PIV) turbulent data. The analysis derives a 2nd order random field over the whole flow domain that gives better turbulence properties in areas of non-uniform flow and where flow separates than the present models that are based on the Navier-Stokes Equations. These latter models need assumptions to decrease the number of calculations to enable them to run on present day computers or super-computers. These assumptions reduce the accuracy of these models. The improved flow field is gained at the expense of the model not being generic. Therefore the new data driven model can only be used for the flow situation of the data as the analysis shows that the kernel of the turbulent flow field of undular hydraulic jump could not be related to the surface waves, a key feature of the jump. The kernel developed has two parts, called the outer and inner parts. A comparison shows that the ratio of outer kernel to inner kernel primarily reflects the ratio of turbulent production to turbulent dissipation. The outer part, with a larger correlation length, reflects the larger structures of the flow that contain most of the turbulent energy production. The inner part reflects the smaller structures that contain most turbulent energy dissipation. The new data driven model can use a kernel with changing variance and/or regression coefficient over the domain, necessitating the use of both numerical and analytical methods. The model allows the use of a two-part regression coefficient kernel, the solution being the addition of the result from each part of the kernel. This research highlighted the need to assess the size of the structures calculated by the models based on the Navier-Stokes equations to validate these models. At present most studies use mean velocities and the turbulent fluctuations to validate a models performance. As the new data driven model gives better turbulence properties, it could be used in complicated flow situations, such as a rock groyne to give better assessment of the forces and pressures in the water flow resulting from turbulence fluctuations for the design of such structures. Further development to make the model usable includes; solving the numerical problem associated with the double kernel, reducing the number of modes required, obtaining a solution for the kernel of two-dimensional and three-dimensional flows, including the change in correlation length with time as presently the model gives instant realisations of the flow field and finally including third and fourth order statistics to improve the data driven model velocity field from having Gaussian distribution properties. As the third and fourth order statistics are Reynolds Number dependent this will enable the model to be applied to PIV data from physical scale models. In summary, this new data driven model is complementary to models based on the Navier-Stokes equations by providing better results in complicated design situations. Further research to develop the new model is viewed as an important step forward in the analysis of river control structures such as rock groynes that are prevalent on New Zealand Rivers protecting large cities.

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Books on the topic "Stochastic Navier-Stokes"

1

Kolmogorov Equations for Stochastic PDEs (Advanced Courses in Mathematics - CRM Barcelona). Birkhäuser Basel, 2005.

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Prato, Giuseppe Da. Kolmogorov Equations For Stochastic Pdes (Advanced Courses in Mathematics, Crm Barcelona). Birkhauser, 2004.

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Book chapters on the topic "Stochastic Navier-Stokes"

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Adomian, George. "The Navier-Stokes Equations." In Nonlinear Stochastic Systems Theory and Application to Physics, 192–215. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2569-4_18.

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Sritharan, S. S. "Nonlinear Filtering of Stochastic Navier-Stokes Equation." In Nonlinear Stochastic PDEs, 247–60. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4613-8468-7_14.

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Gallavotti, Giovanni. "Reversible Viscosity and Navier–Stokes Fluids." In Stochastic Dynamics Out of Equilibrium, 569–80. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15096-9_21.

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Da Prato, Giuseppe. "The Stochastic 2D Navier—Stokes Equation." In Kolmogorov Equations for Stochastic PDEs, 155–72. Basel: Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7909-5_6.

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Flandoli, Franco. "Remarks on Stochastic Navier-Stokes Equations." In Mathematical Paradigms of Climate Science, 51–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-39092-5_4.

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Breit, Dominic. "An Introduction to Stochastic Navier–Stokes Equations." In New Trends and Results in Mathematical Description of Fluid Flows, 1–51. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-94343-5_1.

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Arnaudon, Marc, and Ana Bela Cruzeiro. "Stochastic Lagrangian Flows and the Navier–Stokes Equations." In Stochastic Analysis: A Series of Lectures, 55–75. Basel: Springer Basel, 2015. http://dx.doi.org/10.1007/978-3-0348-0909-2_2.

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Crauel, Hans, and Franco Flandoli. "Dissipativity of Three-Dimensional Stochastic Navier-Stokes Equation." In Seminar on Stochastic Analysis, Random Fields and Applications, 67–76. Basel: Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-7026-9_5.

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Chow, P. L. "Stationary Solutions of Two-Dimensional Navier-Stokes Equations with Random Perturbation." In Nonlinear Stochastic PDEs, 237–45. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4613-8468-7_13.

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Méléard, Sylvie. "Stochastic Particle Approximations for Two-Dimensional Navier-Stokes Equations." In Dynamics and Randomness II, 147–97. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2469-6_5.

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Conference papers on the topic "Stochastic Navier-Stokes"

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THOMANN, ENRIQUE, and MINA OSSIANDER. "STOCHASTIC CASCADES APPLIED TO THE NAVIER-STOKES EQUATIONS." In Proceedings of the Swansea 2002 Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812703989_0019.

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CUTLAND, NIGEL J. "STOCHASTIC NAVIER–STOKES EQUATIONS: LOEB SPACE TECHNIQUES & ATTRACTORS." In Proceedings of the Swansea 2002 Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812703989_0007.

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CARABALLO, T. "THE LONG-TIME BEHAVIOUR OF STOCHASTIC 2D-NAVIER-STOKES EQUATIONS." In Proceedings of the Swansea 2002 Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812703989_0005.

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Brzeźniak, Zdzisław, and Yu-Hong Li. "Asymptotic behaviour of solutions to the 2D stochastic Navier-Stokes equations in unbounded domains —new developments." In Proceedings of the First Sino-German Conference on Stochastic Analysis (A Satellite Conference of ICM 2002). WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702241_0006.

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Naitoh, Ken, Korai Ryu, Shinichi Tanaka, Shunsuke Matsushita, Mitsuaki Kurihara, and Mikiya Marui. "Weakly-stochastic Navier-Stokes Equation and Shocktube Experiments: Revealing the Reynolds' Mystery in Pipe Flows." In 42nd AIAA Fluid Dynamics Conference and Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2012. http://dx.doi.org/10.2514/6.2012-2689.

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Bensoussan, A. "A model of stochastic differential equation in Hilbert applicable to Navier-Stokes equation in dimension 2." In 29th IEEE Conference on Decision and Control. IEEE, 1990. http://dx.doi.org/10.1109/cdc.1990.204043.

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Walters, D. Keith, and William H. Luke. "3-D Navier-Stokes Simulation of Large-Scale Regions of the Bronchopulmonary Tree." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12856.

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A new methodology for CFD simulation of airflow in the human bronchopulmonary tree is presented. The new approach provides a means for detailed resolution of the flow features via three-dimensional Navier-Stokes CFD simulation without the need for direct simulation of the entire flow geometry, which is well beyond the reach of available computing power now and in the foreseeable future. The method is based on a finite number of flow paths, each of which is fully resolved, to provide a detailed description of the entire complex small-scale flowfield. A stochastic coupling approach is used for the unresolved flow path boundary conditions, yielding a virtual flow geometry allowing accurate statistical resolution of the flow at all scales for any set of flow conditions. Results are presented for multi-generational lung models based on the Weibel morphology and the anatomical data of Hammersley and Olson. Validation simulations are performed for a portion of the bronchiole region (generations 4–12) using the flow path ensemble method, and compared to simulations that are geometrically fully resolved. Results are obtained for three inspiratory flowrates and compared in terms of pressure drop, flow distribution characteristics, and flow structure. Results show excellent agreement with the fully resolved geometry, while reducing the mesh size and computational cost by as much as 94%.

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Naitoh, Ken, Tsuyoshi Nogami, and Takahiro Tobe. "An approach for finding quantum leap of drag reduction: based on the weakly-stochastic Navier-Stokes equation." In 43rd AIAA Fluid Dynamics Conference. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-2464.

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Naruse, Koki, and Ken Naitoh. "Spatial transition point from laminar flow to turbulence in a pipe with injection revealed by solving a weakly-stochastic Navier-Stokes equation." In 2018 AIAA Aerospace Sciences Meeting. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-0589.

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Kijima, Hiroki, Ken Naitoh, Tomotaka Kobayashi, and Yuya Yamashita. "Spatial transition point from laminar flow to turbulence in a circular pipe with bellmouth inlet by solving a weakly-stochastic Navier-Stokes equation." In AIAA Scitech 2021 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2021. http://dx.doi.org/10.2514/6.2021-0631.

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Reports on the topic "Stochastic Navier-Stokes"

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Mikulevicius, R., and B. Rozovskii. Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada413558.

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Tran, Hoang, Catalin Trenchea, and Clayton Webster. A convergence analysis of stochastic collocation method for Navier-Stokes equations with random input data. Office of Scientific and Technical Information (OSTI), January 2014. http://dx.doi.org/10.2172/1649669.

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