Asymptotic behaviour of the three-dimensional α-Navier–Stokes model with delays

We prove the existence and exponential stability of the stationary solutions for a three-dimensional α-Navier–Stokes model with delays. Instead of working directly with the model, we establish the results for a general abstract delay model, and then we apply them to our particular situation. We use two techniques in the stability analysis: the Lyapunov and Razumikhin approaches.