@incollection{AST_2011__339__137_0,
author = {Kupiainen, Antti},
title = {Ergodicity of two dimensional turbulence [after {Hairer} and {Mattingly]}},
booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
series = {Ast\'erisque},
note = {talk:1016},
pages = {137--156},
year = {2011},
publisher = {Soci\'et\'e math\'ematique de France},
number = {339},
zbl = {1356.76003},
language = {en},
url = {https://www.numdam.org/item/AST_2011__339__137_0/}
}
TY - CHAP AU - Kupiainen, Antti TI - Ergodicity of two dimensional turbulence [after Hairer and Mattingly] BT - Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026 AU - Collectif T3 - Astérisque N1 - talk:1016 PY - 2011 SP - 137 EP - 156 IS - 339 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2011__339__137_0/ LA - en ID - AST_2011__339__137_0 ER -
%0 Book Section %A Kupiainen, Antti %T Ergodicity of two dimensional turbulence [after Hairer and Mattingly] %B Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026 %A Collectif %S Astérisque %Z talk:1016 %D 2011 %P 137-156 %N 339 %I Société mathématique de France %U https://www.numdam.org/item/AST_2011__339__137_0/ %G en %F AST_2011__339__137_0
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.. https://www.numdam.org/item/AST_2011__339__137_0/
[1] , , & - "On finite-dimensional projections of distributions for solutions of randomly forced Navier-Stokes equations", Ann. Inst. H. Poincaré Probab. Statist. 43 (2007), p. 399-415. | MR | Zbl | EuDML | DOI
[2] & - "Navier-Stokes equations: controllability by means of low modes forcing", J. Math. Fluid Mech. 7 (2005), p. 108-152. | MR | Zbl | DOI
[3] - "Influence of friction on the direct cascade of forced turbulence", Europhys. Lett. 50 (2000), p. 333-339. | DOI
[4] , , & - "Inverse turbulent cascades and conformally invariant curves", Phys. Rev. Lett. 98 (2007), 024501. | DOI
[5] - "Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence", Journal of Fluid Mechanics 589 (2007), p. 253-260. | Zbl | DOI
[6] , & - "Exponential mixing of the stochastic Navier-Stokes dynamics", Comm. Math. Phys. 230 (2002), p. 87-132. | MR | Zbl | DOI
[7] & - "Inviscid limit for damped and driven incompressible Navier-Stokes equations in ", Comm. Math. Phys. 275 (2007), p. 529-551. | MR | Zbl | DOI
[8] & - Ergodicity for infinite-dimensional systems, London Math. Soc. Lecture Note Series, vol. 229, Cambridge Univ. Press, 1996. | MR | Zbl
[9] & - "Ergodicity for the Navier-Stokes equation with degenerate random forcing: finite-dimensional approximation", Comm. Pure Appl. Math. 54 (2001), p. 1386-1402. | MR | Zbl | DOI
[10] , & - "Gibbsian dynamics and ergodicity for the stochastically forced Navier-Stokes equation", Comm. Math. Phys. 224 (2001), p. 83-106. | MR | Zbl | DOI
[11] - "Dissipativity and invariant measures for stochastic Navier-Stokes equations", NoDEA Nonlinear Differential Equations Appl. 1 (1994), p. 403-423. | MR | Zbl | DOI
[12] - Turbulence, Cambridge Univ. Press, 1995. | MR | Zbl | DOI
[13] & - "Ergodicity of the Navier-Stokes equations with degenerate stochastic forcing", Ann. of Math. 164 (2006), p. 993-1032. | MR | Zbl | DOI
[14] & , "Spectral gaps in Wasserstein distances and the stochastic Navier-Stokes equations", Ann. Probab. 36 (2008), p. 2050-2091. | MR | Zbl | DOI
[15] & , "A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs", preprint arXiv:0808.1361. | MR | Zbl | DOI
[16] - "Inertial ranges in two dimensional turbulence", Phys. Fluids 10 (1967), p. 1417-1423. | DOI
[17] - Randomly forced nonlinear and statistical hydrodynamics in space dimensions, Zürich Lectures in Adv. Math., European Math. Soc. (EMS), Zürich, 2006. | MR | Zbl
[18] & - "Ergodicity for the randomly forced Navier-Stokes equations", Math. Phys. Anal. Geom. 4 (2001), p. 147-195. | MR | Zbl | DOI
[19] - "Statistical theories of turbulence", in Random Media 2000 (J. Wehr, éd.), Wydawnictwa ICM, Warszawa, 2004.
[20] - "Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics", Comm. Math. Phys. 230 (2002), p. 421-462. | MR | Zbl | DOI
[21] & - "Malliavin calculus for the stochastic Navier-Stokes equation", Comm. Pure Appl. Math. 59 (2006), p. 1742-1790. | MR | Zbl | DOI
[22] & - "Global -solutions of stochastic Navier-Stokes equations", Ann. Probab. 33 (2005), p. 137-176. | MR | Zbl | DOI
[23] - "Simplified Malliavin calculus", in Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, 1986, p. 101-130. | MR | Zbl | EuDML | Numdam | DOI
[24] - The Malliavin calculus and related topics, Probability and its Applications, Springer, 1995. | MR | Zbl | DOI
[25] , , & - "Energy and enstrophy transfer in decaying two-dimensional turbulence", Phys. Rev. Lett. 90 (2003), 104502. | DOI







