Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations

Details Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations

2010-02-10

arxiv.org/abs/1002.2176v2

Mathematics

Optimization and Control

25 pages

Scientific paper

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 also the full Navier-Stokes system.

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