arXiv:2604.15846v2 Announce Type: replace-cross Abstract: This paper develops and analyzes a computationally efficient receding horizon control (RHC) strategy for steering two-dimensional Navier--Stokes flows to prescribed reference trajectories. The control is represented by a finite linear combination of localized actuators supported within a prescribed control subdomain. At the continuous PDE level, we establish local exponential stabilization in the $L^2$-norm and suboptimality of the actuator-based RHC scheme for weak solutions. Direct implementation requires the repeated solution of high-dimensional finite-horizon optimal control problems. To reduce this computational cost, we combine RHC with model order reduction based on proper orthogonal decomposition (POD). A common POD space constructed from state snapshots reduces the state and adjoint equations and accelerates the online optimization, while the resulting controls are applied to the full-order discretized dynamics. Numerical experiments for two flow configurations of increasing complexity examine the influence of actuator layouts, prediction horizons, viscosity, and POD dimension. The numerical results demonstrate substantial reductions in computational cost while maintaining closed-loop stabilization in the tested configurations.