Lp Exponential Stability for the Equilibrium Solutions of the Navier-Stokes Equations

The exponential stability of the solution of the Navier-Stokes equation in Lp, p > 2, p ≠ 3, in bounded domain is considered in this paper. Under some assumptions on the external force, it can be shown that the bounded solution of the Navier-Stokes equation with initial and boundary conditions approaches the stationary solution of the system exponentially when time t goes to infinite.