AN ERROR ESTIMATE UNIFORM IN TIME FOR SPECTRAL SEMI-GALERKIN APPROXIMATIONS OF THE NONHOMOGENEOUS NAVIER-STOKES EQUATIONS

We consider the spectral semi-Galerkin method applied to the non-homogeneous Navier-Stokes equations, which describes the motion of miscibles fluids. Under certain conditions it is known that the aproximate solutions constructed by using this method converge to a global strong solution of these equations. In this paper we prove that these solutions satisfy an optimal uniform in time error estimate in the H1-norm for the velocity. We also derive an uniform error estimate in the L(infinity)-norm for the density and an improved error estimate in the L2-norm for the velocity.