Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations
Optimization and Control
2010-09-20 v2 Analysis of PDEs
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 also the full Navier-Stokes system.
Cite
@article{arxiv.1002.2176,
title = {Internal exponential stabilization to a non-stationary solution for 3D Navier-Stokes equations},
author = {Viorel Barbu and Sergio S. Rodrigues and Armen Shirikyan},
journal= {arXiv preprint arXiv:1002.2176},
year = {2010}
}
Comments
25 pages