Math @ Duke

Publications [#303550] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 Hairer, M; Mattingly, JC; Pardoux, E, Malliavin calculus and ergodic properties of highly degenerate 2D stochastic Navierâ€“Stokes equation,
arXiv preprint math/0409057
(2004) [0409057v1]
(last updated on 2018/10/14)
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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