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Publications [#10349] of Jonathan C. Mattingly
search arxiv.org.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.
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