Dirichlet quotients and 2D periodic Navier-Stokes equations

AbstractWe show that for the periodic 2D Navier-Stokes equations (NSE) the set of initial data for which the solution exists for all negative times and has exponential growth is rather rich. We study this set and show that it is dense in the phase space of the NSE. This yields to a positive answer to a question in [BT]. After an appropriate rescaling the large Reynolds limit dynamics on this set is Eulerian