Abstract: This paper is concerned with the large time behavior of the modified Navier-Stokes equations in Rⁿ . By improving the Fourier splitting methods, it is proved that the weak solution decays in L² norm at the rate (1+t)^n/4 when the initial data u_0∈ L²∩L¹. Moreover, the error estimate between modified Navier-Stokes equations and classic Navier-Stokes equations is studied.

Key words: Decay rate, Fourier splitting, Navier-Stokes equations.