On the uniqueness of strong solution to the incompressible Navier–Stokes equations with damping

In this paper, we show that the Cauchy problem of the incompressible Navier–Stokes equations with damping α | u | β − 1 u ( α > 0 ) has global strong solution for any β > 3 and the strong solution is unique when 3 < β ⩽ 5 . This improves earlier results.