Publications [#243844] of Jonathan C. Mattingly
- Mattingly, JC, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics,
Communications in Mathematical Physics, vol. 230 no. 3
pp. 421-462, ISSN 0010-3616 [MR2004a:76039], [pdf], [doi]
(last updated on 2019/02/20)
We prove that the two dimensional Navier-Stokes equations possess 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 examine the ergodic theory of the non-Markovian processes.