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

Abstract 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 .

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