Decay and the asymptotic behavior of solutions to the 3D incompressible Navier–Stokes equations with damping.

This paper studies the decay and the asymptotic behavior of solutions to the 3D incompressible Navier–Stokes equations with nonlinear damping α | u | β − 1 u (α > 0 , β > 1). We will prove the L 2 decay of weak solutions for β > 1 with any α > 0. Moreover, we concern the asymptotic stability of the solutions to the system for β > 1 with any α > 0. [ABSTRACT FROM AUTHOR]