ON THE LARGE TIME GALERKIN APPROXIMATION OF THE NAVIER-STOKES EQUATIONS

The difficult problem of relating the large time behavior of the Navier-Stokes equations to the large time behavior of their Galerkin approximation is considered. Attention is restricted to the simplest situation dealing with stationary solutions and the question is the following one: if the computed approximation of the time dependent equations 'seems to converge' to some limit as approached t yields cent , is the same true for the exact problem and are the limits related? Some sufficient conditions (reasonably easy to verify) which guarantee a positive answer to this question are given.