Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together with L-p - L-q estimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations as C-1(1 + t)(-3/4) <= parallel to u parallel to(L2) (1 + t)(-3/4), t > 1. The decay rate is optimal since it coincides with that of heat equation.