211 citations · 257 across the 11 of their papers we have counts for
5 papers · 1 filter
On Recent Progress for the Stochastic Navier Stokes Equations
Jonathan C. Mattingly
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 par…
Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navier--Stokes equation
Martin Hairer, Jonathan C. Mattingly, Etienne Pardoux
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 dimensio…
The Small Scales of the Stochastic Navier Stokes Equations under Rough Forcing
Jonathan C. Mattingly, Toufic M. Suidan
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 ge…
Malliavin Calculus for the Stochastic 2D Navier Stokes Equation
Jonathan C. Mattingly, Etienne Pardoux
We consider the incompressible, two dimensional Navier Stokes equation with periodic boundary conditions under the effect of an additive, white in time, stochastic forcing. Under m…
Ergodicity of the 2D Navier-Stokes Equations with Degenerate Stochastic Forcing
Martin Hairer, Jonathan C. Mattingly
The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that t…