2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102188We consider the spectral semi-Galerkin method applied to the nonhomogeneous Navier-Stokes equations. Under certain conditions it is known that the approximate solutions constructed through this method converge to a global strong solution of these equations. Here, we derive an optimal uniform in time error estimate in the $H^1$ norm for the velocity. We also derive an error estimate for the density in some spaces $L^r$.22 pages; Some typos were correctedAnalysis of PDEs35Q35; 65M15; 65M60;76D99text