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

Abstract

The incompressible Navier–Stokes equations with damping are considered in this paper. Using Fourier splitting method, we will prove the L 2 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 ≥ 1 2 as β = 3 .