Math @ Duke

Publications [#139692] of Jonathan C. Mattingly
Preprints
 Martin Hairer, Jonathan C. Mattingly, Etienne Pardoux, Malliavin calculus and ergodic properties of highly degenerate 2D stochastic NavierStokes equation,
Comptes rendus Mathematique (CRAS), In press
(Summer, 2004) [math.PR/0409057]
(last updated on 2007/12/16)
Author's Comments: A condensed version of the two CRAS notes.
Abstract: The objective of this note is to present the
results from the two recent papers. We study
the NavierStokes equation on the
twodimensional torus when forced by a
finite dimensional white Gaussian noise. We
give conditions under which both the law of
the solution at any time t>0, projected on a
finite dimensional subspace, has a smooth
density with respect to Lebesgue measure and
the solution itself is ergodic. In
particular, our results hold for specific
choices of four dimensional white Gaussian
noise. Under additional assumptions, we show
that the preceding density is everywhere
strictly positive.


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