Ergodicity and mixing for stochastic partial differential equations
| dc.creator | Bricmont, Jean | |
| dc.date | 2002-12-01 | |
| dc.date.accessioned | 2026-07-07T04:54:11Z | |
| dc.date.available | 2026-07-07T04:54:11Z | |
| dc.description | Recently, a number of authors have investigated the conditions under which a stochastic perturbation acting on an infinite dimensional dynamical system, e.g. a partial differential equation, makes the system ergodic and mixing. In particular, one is interested in finding minimal and physically natural conditions on the nature of the stochastic perturbation. I shall review recent results on this question; in particular, I shall discuss the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity $ν$, and grows like $ν^{-3}$ when $ν$ goes to zero. This Markov process has a unique invariant measure and is exponentially mixing in time. | |
| dc.identifier | https://arxiv.org/abs/math/0212412 | |
| dc.identifier | http://arxiv.org/abs/math/0212412 | |
| dc.identifier | Proceedings of the ICM, Beijing 2002, vol. 1, 567--585 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66149 | |
| dc.subject | Probability | |
| dc.subject | 35Q30, 60H15 | |
| dc.title | Ergodicity and mixing for stochastic partial differential equations | |
| dc.type | text |