Math @ Duke

Publications [#243844] of Jonathan C. Mattingly
search arxiv.org.Papers Published
 Mattingly, JC, Exponential convergence for the stochastically forced NavierStokes equations and other partially dissipative dynamics,
Communications in Mathematical Physics, vol. 230 no. 3
(2002),
pp. 421462, ISSN 00103616 [MR2004a:76039], [pdf], [doi]
(last updated on 2021/10/24)
Abstract: We prove that the two dimensional NavierStokes equations possess an exponentially attracting invariant measure. This result is in fact the consequence of a more general "Harrislike" 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 "Doeblinlike" theorem is proven. One of the main features of this paper is the novel coupling construction used to examine the ergodic theory of the nonMarkovian processes.


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