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Remarks on determining projections for stochastic dissipative equations
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.