A NEW MODIFIED GALERKIN METHOD FOR THE TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS

摘要

The nonlinear Galerkin method as well as the postprocessed Galerkin method were built upon the notion of approximate inertial manifold (a.i.m.). We conceived a modified Galerkin method that uses the so-called ”induced trajectories” defined in [19], instead of the a.i.m.s. The paper presents this new method, that provides a sequence of func- tions approximating the solution of the Navier Stokes equations. The convergence of this sequence of functions to the exact solution is proved and some comments on the relationship between our method and the nonlinear postprocessed Galerkin method are given.