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Internal exponential stabilization to a nonstationary solution for 3D Navier-Stokes equations. (English) Zbl 1231.35141

Authors’ abstract: We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and stabilizes the linearized equation. The proof of this fact is based on a truncated observability inequality, the regularizing property for the linearized equation, and some standard techniques of the optimal control theory. We then show that the control constructed for the linear problem stabilizes locally the full Navier-Stokes system.

MSC:

35Q30 Navier-Stokes equations
93D15 Stabilization of systems by feedback
93B52 Feedback control
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