Existence and uniqueness of solutions for the Navier–Stokes equations with hyperdissipation

The Navier–Stokes equations with hyperdissipation are used to numerically simulate turbulent flows. While numerical aspects of this model are well-understood, its analytic properties have not been thoroughly explored. In this article, we prove the existence and uniqueness of strong solutions to these equations on T2 with periodic boundary conditions. Our proof extends the methods of Cannone (1995) and Cannone and Meyer (1995) to the discrete setting and relies on Littlewood–Paley theory and techniques from multiple Fourier series.  2003 Elsevier Science (USA). All rights reserved