Asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term

This paper deals with the asymptotic behavior of strong solutions to the 3D Navier–Stokes equations with a nonlinear damping term |u|β−1u(β≥3)|u|β−1u(β≥3). First, we establish an upper bound for the difference between the solution of our equation and the heat equation in L2L2 space. Then, we optimize the upper bound of decay for the solutions and obtain their algebraic lower bound by using Fourier Splitting method.