Time-periodic strong solutions of the 3D Navier-Stokes equations with damping

Abstract

This article concerns the incompressible Navier-Stokes equations with damping and homogeneous Dirichlet boundary conditions in 3D bounded domains. We find conditions on parameters to guarantee that the problem has a strong time-periodic solution and that the weak solutions of the problem converge to a unique time-periodic solution as t → ∞.