An error estimate uniform in time for spectral Galerkin approximations of the Navier-Stokes problem

The existence theory for the nonstationary Navier-Stokes equations can be developed, by the method of Galerkin approximation, using any of a wide variety of possible systems of basis functions. The basis functions used in the papers of Hopf [8] and of Kiselev and Ladyzhenskaya [10] are merely assumed to belong to and be complete in certain function spaces. However, to obtain refinements in the theory by the Galerkin method, particularly regarding the regularity and decay of solutions, it often appears essential to choose as basis functions the eigenf unctions of the Stokes operator; see Ito and Hey wood [4,