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.
Nonlinear Analysis, Theory, Methods and Applications
Lasiecka, I., & Triggiani, R. (2015). Stabilization to an equilibrium of the Navier-Stokes equations with tangential action of feedback controllers. Nonlinear Analysis, Theory, Methods and Applications, 121, 424-446. https://doi.org/10.1016/j.na.2015.03.012