J. Bricmont, A. Kupiainen, and R. Lefevere, Ergodicity of the 2D Navier--Stokes Equations??with Random Forcing, Communications in Mathematical Physics, vol.224, issue.1, pp.65-81, 2001.
DOI : 10.1007/s002200100510

C. [. Baiesi and . Maes, Enstrophy dissipation in two-dimensional turbulence, Physical Review E, vol.72, issue.5, pp.56314-56321, 2005.
DOI : 10.1103/PhysRevE.72.056314

URL : http://arxiv.org/abs/cond-mat/0505643

]. A. Bor13 and . Boritchev, Estimates for solutions of a low-viscosity kick-forced generalized Burgers equation, Proc. Roy. Soc. Edinburgh Sect. A, vol.143, issue.2, pp.253-268, 2013.

J. L. Doob, Asymptotic Properties of Markoff Transition Probabilities, Transactions of the American Mathematical Society, vol.63, issue.3, pp.393-421, 1948.
DOI : 10.2307/1990566

J. [. Da-prato and . Zabczyk, Ergodicity for Infinite Dimensional Systems, 1996.
DOI : 10.1017/CBO9780511662829

[. Eckmann and M. Hairer, Non-Equilibrium Statistical Mechanics??of Strongly Anharmonic Chains of Oscillators, Communications in Mathematical Physics, vol.212, issue.1, pp.105-164, 2000.
DOI : 10.1007/s002200000216

]. Epr99a, C. Eckmann, L. Pillet, and . Rey-bellet, Entropy production in nonlinear, thermally driven Hamiltonian systems, J. Statist. Phys, vol.95, issue.12, pp.305-331, 1999.

D. [. Evans and . Searles, Equilibrium microstates which generate second law violating steady states, Physical Review E, vol.50, issue.2, pp.1645-1648, 1994.
DOI : 10.1103/PhysRevE.50.1645

P. Gaspard, Time-reversed dynamical entropy and irreversibility in markovian random processes, J. Statist. Phys, vol.117, pp.3-4, 2004.
DOI : 10.1007/s10955-004-3455-1

E. [. Gallavotti and . Cohen, Dynamical ensembles in stationary states, Journal of Statistical Physics, vol.78, issue.3, pp.5-6, 1995.
DOI : 10.1007/BF02179860

URL : http://arxiv.org/abs/chao-dyn/9501015

M. Gourcy, A large deviation principle for 2D stochastic Navier? Stokes equation, Stochastic Process, Appl, vol.117, issue.7, pp.904-927, 2007.
DOI : 10.1016/j.spa.2006.11.001

URL : http://doi.org/10.1016/j.spa.2006.11.001

?. I. G¯-ihman and A. V. Skorohod, The Theory of Stochastic Processes . I, 1980.

G. [. Ginibre and . Velo, The Cauchy problem in local spaces for the complex Ginzburg-Landau equation. I. Compactness methods, Phys, pp.3-4, 1996.

V. [. Jak?i´jak?i´c, C. Nersesyan, A. Pillet, and . Shirikyan, Large deviations from a stationary measure for a class of dissipative PDE's with random kicks, 2012.

C. [. Jak?i´jak?i´c, L. Pillet, and . Rey-bellet, Entropic fluctuations in statistical mechanics: I. Classical dynamical systems, Nonlinearity, vol.24, issue.3, pp.699-763, 2011.
DOI : 10.1088/0951-7715/24/3/003

]. S. Kru69 and . Kru?kov, The Cauchy problem for certain classes of quasilinear parabolic equations, Mat. Zametki, vol.6, pp.295-300, 1969.

A. [. Kuksin and . Shirikyan, Mathematics of Two-Dimensional Turbulence
DOI : 10.1017/CBO9781139137119

J. Kurchan, Fluctuation theorem for stochastic dynamics, Journal of Physics A: Mathematical and General, vol.31, issue.16, pp.3719-3729, 1998.
DOI : 10.1088/0305-4470/31/16/003

]. V. Lav07, C. Lecomte, F. Appert-rolland, and . Van-wijland, Thermodynamic formalism for systems with Markov dynamics, J. Stat. Phys, vol.127, issue.1, pp.51-106, 2007.

H. [. Lebowitz and . Spohn, A Gallavotti-Cohen-type symmetry in the large deviation functional for stochastic dynamics, Journal of Statistical Physics, vol.95, issue.1/2, pp.333-365, 1999.
DOI : 10.1023/A:1004589714161

C. Maes, The fluctuation theorem as a Gibbs property, Journal of Statistical Physics, vol.95, issue.1/2, pp.367-392, 1999.
DOI : 10.1023/A:1004541830999

]. G. Mét78 and . Métivier, Valeurs propres d'opérateurs définis par la restriction de systèmes variationnelsàvariationnelsà des sous-espaces, J. Math. Pures Appl, vol.57, issue.9 2, pp.133-156, 1978.

K. [. Maes and . Neto?n´neto?n´y, Time-reversal and entropy, Journal of Statistical Physics, vol.110, issue.1/2, pp.269-310, 2003.
DOI : 10.1023/A:1021026930129

F. [. Maes, M. Redig, and . Verschuere, From global to local fluctuation theorems, Mosc. Math. J, vol.1, issue.3, pp.421-438, 2001.

D. Novikov, Hahn decomposition and Radon-Nikodym theorem with a parameter, 2005.

C. [. Rondoni and . Mejía-monasterio, Fluctuations in nonequilibrium statistical mechanics: models, mathematical theory, physical mechanisms, Nonlinearity, vol.20, issue.10, pp.1-37, 2007.
DOI : 10.1088/0951-7715/20/10/R01

L. [. Rey-bellet and . Thomas, Fluctuations of the Entropy Production in Anharmonic Chains, Annales Henri Poincar??, vol.3, issue.3, pp.483-502, 2002.
DOI : 10.1007/s00023-002-8625-6

D. Ruelle, Entropy Production in Nonequilibrium Statistical Mechanics, Communications in Mathematical Physics, vol.189, issue.2, pp.365-371, 1997.
DOI : 10.1007/s002200050207

]. M. Tay97 and . Taylor, Partial Differential Equations. I?III, pp.1996-97

R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 1988.

F. B. Weissler, Local existence and nonexistence for semilinear parabolic equations in L p , Indiana Univ, Math. J, vol.29, issue.1, pp.79-102, 1980.

]. L. Wu01 and . Wu, Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems

A. M. Yaglom, The ergodic principle for Markov processes with stationary distributions, Doklady Akad, Nauk SSSR (N.S.), vol.56, pp.347-349, 1947.