On the Kolmogorov entropy of the weak global attractor of 3D Navier-Stokes equations:I

One particular metric that generates the weak topology on the weak global attractor \begin{document}$\mathcal{A}_w$\end{document} of three dimensional incompressible Navier-Stokes equations is introduced and used to obtain an upper bound for the Kolmogorov entropy of \begin{document}$\mathcal{A}_w$\end{document} . This bound is expressed explicitly in terms of the physical parameters of the fluid flow.