| Chen, Le, Ouyang, Cheng, Tindel, Samy and Xia, Panqiu 2025. On ergodic properties of stochastic PDEs. Stochastics and Partial Differential Equations: Analysis and Computations 10.1007/s40072-025-00365-0 |
Abstract
In this note we review several situations in which stochastic PDEs exhibit ergodic properties. We begin with the basic dissipative conditions, as stated by Da Prato and Zabczyk in their classical monograph. Then we describe the singular case of SPDEs with reflection. Next we move to some degenerate (and thus more demanding) settings. Namely we recall some results obtained around 2006, concerning stochastic Navier-Stokes equations with a very degenerate noise. We finish the article by handling some cases with degenerate coefficients. This includes a new result about the parabolic Anderson model in dimension , driven by a general class of noises and fairly general initial conditions. In this context, a phase transition is observed, expressed in terms of the noise intensity.
| Item Type: | Article |
|---|---|
| Date Type: | Published Online |
| Status: | In Press |
| Schools: | Schools > Mathematics |
| Publisher: | Springer |
| ISSN: | 2194-0401 |
| Date of Acceptance: | 24 April 2025 |
| Last Modified: | 10 Dec 2025 14:45 |
| URI: | https://orca.cardiff.ac.uk/id/eprint/182960 |
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