# A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case

@article{Foias2012ADF,
title={A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case},
author={Ciprian Foias and Michael S. Jolly and Rostyslav V. Kravchenko and Edriss S. Titi},
journal={Journal of Mathematical Physics},
year={2012},
volume={53},
pages={115623-115623}
}
• Published 27 November 2012
• Mathematics
• Journal of Mathematical Physics
The determining modes for the two-dimensional incompressible Navier-Stokes equations (NSE) are shown to satisfy an ordinary differential equation (ODE) of the form dv/dt = F(v), in the Banach space, X, of all bounded continuous functions of the variable s∈R with values in certain finite-dimensional linear space. This new evolution ODE, named determining form, induces an infinite-dimensional dynamical system in the space X which is noteworthy for two reasons. One is that F is globally Lipschitz…
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