The exponential behavior of Navier-Stokes equations with time delay external force (Q556503)

Existence and exponential behaviour of the solutions to 2D Navier-Stokes equations with time delay external force are discussed. The crucial role of the relations between kinematic viscosity and time delay is shown. For the 3D case the result of Corollary 64.5 of \textit{G. R. Sell} and \textit{Y. You} [Dynamics of Evolutionary Equations, Applied Mathematical Sciences 143. (New York, Springer) (2002; Zbl 1254.37002)] concerning the strong solution is extended. Existence of a periodic solution is discussed.