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

TL;DR

This paper develops explicit time-varying and stationary feedback laws to achieve rapid and null controllability for the 2D incompressible Navier-Stokes equations, enabling small-time local stabilization.

Contribution

It introduces explicit feedback control strategies for rapid stabilization and null controllability of 2D Navier-Stokes equations, with quantifiable costs and convergence times.

Findings

Explicit time-varying feedback laws achieve small-time local stabilization.

Stationary feedback laws enable rapid stabilization with quantifiable rates.

Explicit controls for null controllability have costs bounded by $e^{C/T}$.

Abstract

We provide 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.