Small-time local stabilization of the two-dimensional incompressible Navier–Stokes equations

Abstract

We construct explicit time-varying feedback laws that locally stabilize the two-dimensional internal controlled incompressible Navier–Stokes equations in arbitrarily small time. We also obtain quantitative rapid stabilization via stationary feedback laws, as well as quantitative null-controllability with explicit controls having $e^{C/T}$ costs.