Approximate inertial manifolds for 2D Navier-Stokes equations (Q1191644)

The author finds two new approximate inertial manifolds for 2D Navier- Stokes equations in the periodic case. One is obtained by modifying the spectrum of the Stokes operator in a narrow band so that the new dissipative operator satisfies the standard spectral gap condition, under which the existence of an inertial manifold can be proved. Approximating this manifold by an Euler-Galerkin scheme, one gets another approximate inertial manifold, having some advantages in the numerical sense.