Stochastic dissipative PDE ’ s and Gibbs measures

@inproceedings{Kuksin2000StochasticDP,
  title={Stochastic dissipative PDE ’ s and Gibbs measures},
  author={Sergei Kuksin and Armen Shirikyan},
  year={2000}
}
We study a class of dissipative nonlinear PDE’s forced by a random force η(t, x), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in x and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form 
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References

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Showing 1-10 of 12 references

Ergodicity for Infinite-Dimensional Systems

G. Da Prato, J. Zabczyk
London Mathematical Society Lecture Note Series, vol. 229, Cambridge University Press, Cambridge • 1996
View 4 Excerpts
Highly Influenced

Ergodicity of the 2D Navier-Stokes equation under random perturbations

F. Flandoli, B. Maslowski
Comm. Math. Phys • 1995

Attractors of Evolutionary Equations

A. V. Babin, M. I. Vishik
Studies in Mathematics and its Applications, vol. 25, North-Holland, Amsterdam • 1992

Gevrey class regularity for the solutions of the Navier-Stokes equations

C. Foiaş, R. Temam
J. Funct. Anal • 1989

Stochastic Differential Equations and Diffusion Processes

N. Ikeda, S. Watanabe
North-Holland Mathematical Library, vol. 24, NorthHolland, Amsterdam–New York • 1989

Markov chains

D. Revuz
Second Edition, North-Holland Mathematical Library, vol. 11, North-Holland, Amsterdam–New York • 1984
View 2 Excerpts

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

R. Bowen
Lecture Notes in Mathematics, Vol. 470, Springer-Verlag, Berlin–New York • 1975

Dobrushin, Conditions for the absence of phase transitions in one-dimensional classical systems, Mat. Sb

R L.
1974

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