In　this　article　we　consider　the　spectral　Galerkin　method　with　the　implicit/explicit　Euler　scheme　for　the　two-dimensional　Navier-Stokes　equations　with　the　L-2　initial　data.　Due　to　the　poor　smoothness　of　the　solution　on　[0,　1),　we　use　the　the　spectral　Galerkin　method　based　on　high-dimensional　spectral　space　H-M　and　small　time　step　Delta　t(2)　on　this　interval.　While　on　[1,　infinity),　we　use　the　spectral　Galerkin　method　based　on　low-dimensional　spectral　space　H-m(m　=　O(M-1/2))　and　large　time　step　Delta　t.　For　the　spectral　Galerkin　method,　we　provide　the　standard　H-2-stability　and　the　L-2-error　analysis.　(c)　2007　Wiley　Periodicals,　Inc.