# On recent progress for the stochastic Navier Stokes equations

@inproceedings{Mattingly2003OnRP, title={On recent progress for the stochastic Navier Stokes equations}, author={Jonathan C. Mattingly}, year={2003} }

We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example: the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity…

## 12 Citations

### The Gaussian structure of the singular stochastic Burgers equation

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Abstract We consider the stochastically forced Burgers equation with an emphasis on spatially rough driving noise. We show that the law of the process at a fixed time t, conditioned on no explosions,…

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In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier-Stokes equation (N.S.E.) system on a torus with a degenerate, one dimensional noise. In…

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. We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of ﬂuid equations. These models decompose the deterministic dynamics of interest into fundamental…

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- MathematicsBulletin of the American Mathematical Society
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. Stochastic partial diﬀerential equations are ubiquitous in mathematical modeling. Yet, many such equations are too singular to admit classical treatment. In this article we review some recent…

### Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation

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The objective of this note is to present the results from the two recent papers. We study the Navier--Stokes equation on the two--dimensional torus when forced by a finite dimensional white Gaussian…

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### The Small Scales of the Stochastic Navier–Stokes Equations Under Rough Forcing

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We prove that the small scale structures of the stochastically forced Navier–Stokes equations approach those of the naturally associated Ornstein–Uhlenbeck process as the scales get smaller.…

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