Weak and strong solutions for the incompressible Navier-Stokes equations with damping

In this paper, we show that the Cauchy problem of the Navier-Stokes equations with damping alpha vertical bar u vertical bar(beta-1)u(alpha > 0) has global weak solutions for any beta >= 1, global strong solution for any beta >= 7/2 and that the strong solution is unique for any 7/2 <= beta <= 5. (c) 2008 Elsevier Inc. All rights reserved.