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

Abstract

In this paper, we show that the Cauchy problem of the Navier-Stokes equations with damping α | u |β - 1 u(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.