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.

Publication Title

Nonlinear Analysis, Theory, Methods and Applications