Multi-vortices and lower bounds for the attractor dimension of 2d Navier-Stokes equations

A new method for obtaining lower bounds for the dimension of attractors for the Navier–Stokes equations, which does not use Kolmogorov flows, is presented. Using this method, exact estimates of the dimension are obtained for the case of equations on a plane with Ekman damping. Similar estimates were previously known only for the case of periodic boundary conditions. In addition, similar lower bounds are obtained for the classical Navier–Stokes system in a two-dimensional bounded domain with Dirichlet boundary conditions.