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 α|u|β−1u (α >0) has global weak solutions for any β 1, global strong solution for any β 7/2 and that the strong solution is unique for any 7/2 β 5. © 2008 Elsevier Inc. All rights reserved