Stabilization to an equilibrium of the Navier–Stokes equations with tangential action of feedback controllers

Uniform stabilization in the neighborhood of an unstable equilibrium of the Navier–Stokes equations is considered. It is shown that in 2 and 3 dimensions such equilibrium can be stabilized by purely tangential action of feedback boundary and interior control. The support of such feedback controls can be arbitrarily small—but needs to be localized in a boundary layer. In contrast with prior literature, this result is proved without any assumptions imposed on the spectral properties of the Oseen’s operator, which in turn rest on a unique continuation property.