Remarks on determining projections for stochastic dissipative equations

Luigi C. Berselli; Franco Flandoli

doi:10.3934/dcds.1999.5.197

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1999, Volume 5, Issue 1: 197-214. Doi: 10.3934/dcds.1999.5.197

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Remarks on determining projections for stochastic dissipative equations

Luigi C. Berselli^1, and
Franco Flandoli^2,

1.
Dipartimento di Matematica, Via F. Buonarroti 2, 56126 Pisa
2.
Dipartimento di Matematica Applicata, "U.Dini" Università di Pisa, V.le B. Pisano 26/b, 56126 Pisa

Received: April 1998

Revised: July 1998

Published: January 1999

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Abstract

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.

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Mathematics Subject Classification: 35Q30, 60H15, 35B40, 65D05.

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