Decay of solutions for the 3D Navier-Stokes equations with damping

The incompressible Navier-Stokes equations with damping are considered in this paper. Using Fourier splitting method, we will prove the L2 decay of weak solutions for β>2 with any α>0. Finally, we show the asymptotic stability of the solution to the system for β>3 with any α>0 and α≥12 as β=3.