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January  1999, 5(1): 197-214. doi: 10.3934/dcds.1999.5.197

Remarks on determining projections for stochastic dissipative equations

1. 

Dipartimento di Matematica, Via F. Buonarroti 2, 56126 Pisa, Italy

2. 

Dipartimento di Matematica Applicata, "U.Dini" Università di Pisa, V.le B. Pisano 26/b, 56126 Pisa, Italy

Received  April 1998 Revised  July 1998 Published  October 1998

In this paper we consider the notion of determining projections for two classes of stochastic dissipative equations: a reaction-diffusion equation and a 2-dimensional Navier-Stokes equation.
We define certain finite dimensional objects that can capture the asymptotic behavior of the related dynamical system. They are projections on a space of polynomial functions, generalizing the classical (but not very much studied in a stochastic context) concepts of determining modes, nodes and volumes.
Citation: Luigi C. Berselli, Franco Flandoli. Remarks on determining projections for stochastic dissipative equations. Discrete & Continuous Dynamical Systems - A, 1999, 5 (1) : 197-214. doi: 10.3934/dcds.1999.5.197
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