Agazzi, Andrea; Mattingly, Jonathan C.; Melikechi, Omar Random splitting of fluid models: unique ergodicity and convergence. (English) Zbl 1522.35355 Commun. Math. Phys. 401, No. 1, 497-549 (2023). MSC: 35Q30 35Q31 76D05 34H10 37A05 37A60 PDFBibTeX XMLCite \textit{A. Agazzi} et al., Commun. Math. Phys. 401, No. 1, 497--549 (2023; Zbl 1522.35355) Full Text: DOI arXiv
Zhang, Xicheng; Zhao, Guohuan Stochastic Lagrangian path for Leray’s solutions of 3D Navier-Stokes equations. (English) Zbl 1475.60129 Commun. Math. Phys. 381, No. 2, 491-525 (2021). MSC: 60H30 35Q30 60H15 PDFBibTeX XMLCite \textit{X. Zhang} and \textit{G. Zhao}, Commun. Math. Phys. 381, No. 2, 491--525 (2021; Zbl 1475.60129) Full Text: DOI arXiv
Bedrossian, Jacob; Coti Zelati, Michele; Punshon-Smith, Samuel; Weber, Franziska A sufficient condition for the Kolmogorov 4/5 law for stationary martingale solutions to the 3D Navier-Stokes equations. (English) Zbl 1470.60176 Commun. Math. Phys. 367, No. 3, 1045-1075 (2019). MSC: 60H15 35Q30 35R60 PDFBibTeX XMLCite \textit{J. Bedrossian} et al., Commun. Math. Phys. 367, No. 3, 1045--1075 (2019; Zbl 1470.60176) Full Text: DOI arXiv
Breit, Dominic; Feireisl, Eduard; Hofmanová, Martina Compressible fluids driven by stochastic forcing: the relative energy inequality and applications. (English) Zbl 1362.35228 Commun. Math. Phys. 350, No. 2, 443-473 (2017). Reviewer: Piotr Biler (Wrocław) MSC: 35Q35 76N10 60H15 76M35 PDFBibTeX XMLCite \textit{D. Breit} et al., Commun. Math. Phys. 350, No. 2, 443--473 (2017; Zbl 1362.35228) Full Text: DOI arXiv
Constantin, Peter; Glatt-Holtz, Nathan; Vicol, Vlad Unique ergodicity for fractionally dissipated, stochastically forced 2D Euler equations. (English) Zbl 1294.35078 Commun. Math. Phys. 330, No. 2, 819-857 (2014). MSC: 35Q31 35R11 35A01 35A02 35R60 76D05 PDFBibTeX XMLCite \textit{P. Constantin} et al., Commun. Math. Phys. 330, No. 2, 819--857 (2014; Zbl 1294.35078) Full Text: DOI arXiv
Zhang, Xicheng Stochastic Lagrangian particle approach to fractal Navier-Stokes equations. (English) Zbl 1251.35203 Commun. Math. Phys. 311, No. 1, 133-155 (2012). MSC: 35R60 35Q30 60H30 PDFBibTeX XMLCite \textit{X. Zhang}, Commun. Math. Phys. 311, No. 1, 133--155 (2012; Zbl 1251.35203) Full Text: DOI arXiv
Foias, Ciprian; Hoang, Luan; Nicolaenko, Basil On the helicity in 3D-periodic Navier-Stokes equations. II: The statistical case. (English) Zbl 1184.35239 Commun. Math. Phys. 290, No. 2, 679-717 (2009). MSC: 35Q30 35B10 35B40 35C20 76F02 76M35 PDFBibTeX XMLCite \textit{C. Foias} et al., Commun. Math. Phys. 290, No. 2, 679--717 (2009; Zbl 1184.35239) Full Text: DOI
Kuksin, Sergei B. On distribution of energy and vorticity for solutions of 2D Navier-Stokes equation with small viscosity. (English) Zbl 1168.35034 Commun. Math. Phys. 284, No. 2, 407-424 (2008). MSC: 35Q30 35R60 60H15 76F55 35B45 35B10 PDFBibTeX XMLCite \textit{S. B. Kuksin}, Commun. Math. Phys. 284, No. 2, 407--424 (2008; Zbl 1168.35034) Full Text: DOI
Flandoli, F.; Gubinelli, M.; Hairer, M.; Romito, M. Rigorous remarks about scaling laws in turbulent fluids. (English) Zbl 1140.76011 Commun. Math. Phys. 278, No. 1, 1-29 (2008). MSC: 76F20 76D06 35Q30 PDFBibTeX XMLCite \textit{F. Flandoli} et al., Commun. Math. Phys. 278, No. 1, 1--29 (2008; Zbl 1140.76011) Full Text: DOI arXiv
Cipriano, F.; Cruzeiro, A. B. Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus. (English) Zbl 1120.76013 Commun. Math. Phys. 275, No. 1, 255-269 (2007). MSC: 76D06 35Q30 60H15 PDFBibTeX XMLCite \textit{F. Cipriano} and \textit{A. B. Cruzeiro}, Commun. Math. Phys. 275, No. 1, 255--269 (2007; Zbl 1120.76013) Full Text: DOI
Odasso, Cyril Exponential mixing for the 3D stochastic Navier-Stokes equations. (English) Zbl 1122.60059 Commun. Math. Phys. 270, No. 1, 109-139 (2007). Reviewer: Isamu Dôku (Saitama) MSC: 60H15 76D05 76M35 35R60 37L55 PDFBibTeX XMLCite \textit{C. Odasso}, Commun. Math. Phys. 270, No. 1, 109--139 (2007; Zbl 1122.60059) Full Text: DOI arXiv
Basson, Arnaud Homogeneous statistical solutions and local energy inequality for 3D Navier-Stokes equations. (English) Zbl 1106.76017 Commun. Math. Phys. 266, No. 1, 17-35 (2006). MSC: 76D06 76M35 35Q30 PDFBibTeX XMLCite \textit{A. Basson}, Commun. Math. Phys. 266, No. 1, 17--35 (2006; Zbl 1106.76017) Full Text: DOI
Gomes, Diogo Aguiar A variational formulation for the Navier-Stokes equation. (English) Zbl 1080.37083 Commun. Math. Phys. 257, No. 1, 227-234 (2005). MSC: 37K65 35Q30 76D05 37N10 76M30 93C20 PDFBibTeX XMLCite \textit{D. A. Gomes}, Commun. Math. Phys. 257, No. 1, 227--234 (2005; Zbl 1080.37083) Full Text: DOI
Mattingly, Jonathan C. Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics. (English) Zbl 1054.76020 Commun. Math. Phys. 230, No. 3, 421-462 (2002). MSC: 76D05 35Q30 37H99 37L99 60H10 60H15 76M35 PDFBibTeX XMLCite \textit{J. C. Mattingly}, Commun. Math. Phys. 230, No. 3, 421--462 (2002; Zbl 1054.76020) Full Text: DOI
Masmoudi, Nader; Young, Lai-Sang Ergodic theory of infinite dimensional systems with applications to dissipative parabolic PDEs. (English) Zbl 1009.37049 Commun. Math. Phys. 227, No. 3, 461-481 (2002). MSC: 37L55 37H05 35Q30 76D05 60H05 PDFBibTeX XMLCite \textit{N. Masmoudi} and \textit{L.-S. Young}, Commun. Math. Phys. 227, No. 3, 461--481 (2002; Zbl 1009.37049) Full Text: DOI
Bricmont, J.; Kupiainen, A.; Lefevere, R. Exponential mixing of the 2D stochastic Navier-Stokes dynamics. (English) Zbl 1033.76011 Commun. Math. Phys. 230, No. 1, 87-132 (2002). Reviewer: Yuri E. Gliklikh (Voronezh) MSC: 76D06 60H15 35Q30 PDFBibTeX XMLCite \textit{J. Bricmont} et al., Commun. Math. Phys. 230, No. 1, 87--132 (2002; Zbl 1033.76011) Full Text: DOI arXiv
E, Weinan; Mattingly, J. C.; Sinai, Ya. Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation. (English) Zbl 0994.60065 Commun. Math. Phys. 224, No. 1, 83-106 (2001). Reviewer: J.Jakubowski (Warszawa) MSC: 60H15 35Q30 PDFBibTeX XMLCite \textit{W. E} et al., Commun. Math. Phys. 224, No. 1, 83--106 (2001; Zbl 0994.60065) Full Text: DOI
Bricmont, J.; Kupiainen, A.; Lefevere, R. Ergodicity of the 2D Navier-Stokes equations with random forcing. (English) Zbl 0994.60066 Commun. Math. Phys. 224, No. 1, 65-81 (2001). Reviewer: J.Jakubowski (Warszawa) MSC: 60H15 35Q30 PDFBibTeX XMLCite \textit{J. Bricmont} et al., Commun. Math. Phys. 224, No. 1, 65--81 (2001; Zbl 0994.60066) Full Text: DOI
Mattingly, Jonathan C. Ergodicity of 2D Navier-Stokes equations with random forcing and large viscosity. (English) Zbl 0953.37023 Commun. Math. Phys. 206, No. 2, 273-288 (1999). Reviewer: Hans Crauel (Ilmenau) MSC: 37L55 60H15 76D05 35Q30 PDFBibTeX XMLCite \textit{J. C. Mattingly}, Commun. Math. Phys. 206, No. 2, 273--288 (1999; Zbl 0953.37023) Full Text: DOI
Esposito, R.; Marra, R.; Yau, H. T. Navier-Stokes equations for stochastic particle systems on the lattice. (English) Zbl 0868.60079 Commun. Math. Phys. 182, No. 2, 395-455 (1996). MSC: 60K35 35Q30 82B20 PDFBibTeX XMLCite \textit{R. Esposito} et al., Commun. Math. Phys. 182, No. 2, 395--455 (1996; Zbl 0868.60079) Full Text: DOI
Flandoli, Franco; Maslowski, Bohdan Ergodicity of the 2-D Navier-Stokes equation under random perturbations. (English) Zbl 0845.35080 Commun. Math. Phys. 172, No. 1, 119-141 (1995). MSC: 35Q30 35R60 76D05 PDFBibTeX XMLCite \textit{F. Flandoli} and \textit{B. Maslowski}, Commun. Math. Phys. 172, No. 1, 119--141 (1995; Zbl 0845.35080) Full Text: DOI
Foiaş, Ciprian; Temam, R. Self-similar universal homogeneous statistical solutions of the Navier- Stokes equations. (English) Zbl 0532.60058 Commun. Math. Phys. 90, 187-206 (1983). MSC: 60H99 35Q99 PDFBibTeX XMLCite \textit{C. Foiaş} and \textit{R. Temam}, Commun. Math. Phys. 90, 187--206 (1983; Zbl 0532.60058) Full Text: DOI
Marchioro, C.; Pulvirenti, M. Hydrodynamics in two dimensions and vortex theory. (English) Zbl 0527.76021 Commun. Math. Phys. 84, 483-503 (1982). MSC: 76D05 PDFBibTeX XMLCite \textit{C. Marchioro} and \textit{M. Pulvirenti}, Commun. Math. Phys. 84, 483--503 (1982; Zbl 0527.76021) Full Text: DOI
Inoue, Atsushi; Funaki, Tadahisa On a new derivation of the Navier-Stokes equation. (English) Zbl 0404.35079 Commun. Math. Phys. 65, 83-90 (1979). MSC: 35Q30 35A15 35K10 60H15 35Q05 PDFBibTeX XMLCite \textit{A. Inoue} and \textit{T. Funaki}, Commun. Math. Phys. 65, 83--90 (1979; Zbl 0404.35079) Full Text: DOI
Boldrighini, Carlo; Franceschini, Valter A five-dimensional truncation of the plane incompressible Navier-Stokes equations. (English) Zbl 0394.76031 Commun. Math. Phys. 64, 159-170 (1979). MSC: 76D05 76D99 76-04 PDFBibTeX XMLCite \textit{C. Boldrighini} and \textit{V. Franceschini}, Commun. Math. Phys. 64, 159--170 (1979; Zbl 0394.76031) Full Text: DOI