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Exponential Convergence for the Stochastically Forced Navier-Stokes Equations and Other Partially Dissipative Dynamics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mattingly, Jonathan C. |
| Copyright Year | 2002 |
| Abstract | Abstract: 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. |
| Starting Page | 421 |
| Ending Page | 462 |
| Page Count | 42 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s00220-002-0688-1 |
| Alternate Webpage(s) | http://www.math.duke.edu/~jonm/PaperArchive/01/NsMixing/nsMixing.pdf |
| Alternate Webpage(s) | https://services.math.duke.edu/~jonm/PaperArchive/01/NsMixing/nsMixing.pdf |
| Alternate Webpage(s) | http://www.math.duke.edu/~jonm/PaperArchive/01/NsMixing/nsMixing.ps |
| Alternate Webpage(s) | https://doi.org/10.1007/s00220-002-0688-1 |
| Volume Number | 230 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
