Ergodicity of two dimensional turbulence [after Hairer and Mattingly]
Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1016, 20 p.
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Kupiainen, Antti. Ergodicity of two dimensional turbulence [after Hairer and Mattingly], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1016, 20 p. http://archive.numdam.org/item/AST_2011__339__137_0/

[1] A. A. Agrachev, S. B. Kuksin, A. V. Sarychev & A. Shirikyan - "On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations", Ann. Inst. H. Poincaré Probab. Statist. 43 (2007), p. 399-415. | DOI | EuDML | MR | Zbl

[2] A. A. Agrachev & A. V. Sarychev - "Navier-Stokes equations: controllability by means of low modes forcing", J. Math. Fluid Mech. 7 (2005), p. 108-152. | DOI | MR | Zbl

[3] D. Bernard - "Influence of friction on the direct cascade of 2D forced turbulence", Europhys. Lett. 50 (2000), p. 333-339. | DOI

[4] D. Bernard, G. Boffetta, A. Celani & G. Falkovich - "Inverse turbulent cascades and conformally invariant curves", Phys. Rev. Lett. 98 (2007), 024501. | DOI

[5] G. Boffetta - "Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence", Journal of Fluid Mechanics 589 (2007), p. 253-260. | DOI | Zbl

[6] J. Bricmont, A. Kupiainen & R. Lefevere - "Exponential mixing of the 2D stochastic Navier-Stokes dynamics", Comm. Math. Phys. 230 (2002), p. 87-132. | DOI | MR | Zbl

[7] P. Constantin & F. Ramos - "Inviscid limit for damped and driven incompressible Navier-Stokes equations in 2 ", Comm. Math. Phys. 275 (2007), p. 529-551. | DOI | MR | Zbl

[8] G. Da Prato & J. Zabczyk - Ergodicity for infinite-dimensional systems, London Math. Soc. Lecture Note Series, vol. 229, Cambridge Univ. Press, 1996. | MR | Zbl

[9] E. Weinan & J. C. Mattingly - "Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation", Comm. Pure Appl. Math. 54 (2001), p. 1386-1402. | DOI | MR | Zbl

[10] E. Weinan, J. C. Mattingly & Y. Sinai - "Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation", Comm. Math. Phys. 224 (2001), p. 83-106. | DOI | MR | Zbl

[11] F. Flandoli - "Dissipativity and invariant measures for stochastic Navier-Stokes equations", NoDEA Nonlinear Differential Equations Appl. 1 (1994), p. 403-423. | DOI | MR | Zbl

[12] U. Frisch - Turbulence, Cambridge Univ. Press, 1995. | DOI | MR | Zbl

[13] M. Hairer & J. C. Mattingly - "Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing", Ann. of Math. 164 (2006), p. 993-1032. | DOI | MR | Zbl

[14] M. Hairer & J. C. Mattingly, "Spectral gaps in Wasserstein distances and the 2D stochastic Navier-Stokes equations", Ann. Probab. 36 (2008), p. 2050-2091. | DOI | MR | Zbl

[15] M. Hairer & J. C. Mattingly, "A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs", preprint arXiv:0808.1361. | DOI | MR | Zbl

[16] R. H. Kraichnan - "Inertial ranges in two dimensional turbulence", Phys. Fluids 10 (1967), p. 1417-1423. | DOI

[17] S. B. Kuksin - Randomly forced nonlinear PDEs and statistical hydrodynamics in 2 space dimensions, Zürich Lectures in Adv. Math., European Math. Soc. (EMS), Zürich, 2006. | MR | Zbl

[18] S. B. Kuksin & A. Shirikyan - "Ergodicity for the randomly forced 2D Navier-Stokes equations", Math. Phys. Anal. Geom. 4 (2001), p. 147-195. | DOI | MR | Zbl

[19] A. Kupiainen - "Statistical theories of turbulence", in Random Media 2000 (J. Wehr, éd.), Wydawnictwa ICM, Warszawa, 2004.

[20] J. C. Mattingly - "Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics", Comm. Math. Phys. 230 (2002), p. 421-462. | DOI | MR | Zbl

[21] J. C. Mattingly & É. Pardoux - "Malliavin calculus for the stochastic 2D Navier-Stokes equation", Comm. Pure Appl. Math. 59 (2006), p. 1742-1790. | DOI | MR | Zbl

[22] R. Mikulevicius & B. L. Rozovskii - "Global L 2 -solutions of stochastic Navier-Stokes equations", Ann. Probab. 33 (2005), p. 137-176. | DOI | MR | Zbl

[23] J. Norris - "Simplified Malliavin calculus", in Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, 1986, p. 101-130. | DOI | EuDML | Numdam | MR | Zbl

[24] D. Nualart - The Malliavin calculus and related topics, Probability and its Applications, Springer, 1995. | DOI | MR | Zbl

[25] M. K. Rivera, W. B. Daniel, S. Y. Chen & R. E. Ecke - "Energy and enstrophy transfer in decaying two-dimensional turbulence", Phys. Rev. Lett. 90 (2003), 104502. | DOI