Publications [#10349] of Jonathan C. Mattingly
Papers Published
- Mattingly, Jonathan C., The dissipative scale of the stochastics Navier-Stokes equation: regularization and analyticity,
J. Statist. Phys., vol. 108 no. 5-6
(2002),
pp. 1157--1179 (Dedicated to David Ruelle and Yasha Sinai on
the occasion of their 65th birthdays.) [MR2004e:76035], [pdf]
(last updated on 2005/08/15)Abstract:
We prove that the two dimensional Naiver-Stokes equations posses an exponentially attracting invariant measure. This result is in fact the consequence of a more general "Harris-like" ergodic theorem applicable to many dissipative stochastic PDEs and stochastic processes with memory. A simple iterated map example is also presented to help build intuition and showcase the central ideas in a less encumbered setting. To analyze the iterated map, a general "Doeblin-like" theorem is proven. One of the main features of this paper is the novel coupling construction used to prove the central results.