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- W2006101334 abstract "We study the local exponential stabilization, near a given steady-state flow, of solutions of the Navier–Stokes equations in a bounded domain. The control is performed through a Dirichlet boundary condition. We apply a linear feedback controller, provided by a well-posed infinite-dimensional Riccati equation. We give a characterization of the domain of the closed-loop operator which is obtained from the closed-loop linearized Navier–Stokes system. We give a class of initial data for which a Lyapunov function is obtained. For all $sin[0,1/2[$, the stabilization of the two-dimensional Navier–Stokes equations is proved for initial data in $mathbf{H}^s(Omega)cap V_n^0(Omega)$, where $V_n^0(Omega)$ is the space in which the Stokes operator is defined. We also obtain a three-dimensional stabilization result but only for a very specific set of initial data." @default.
- W2006101334 created "2016-06-24" @default.
- W2006101334 creator A5081799880 @default.
- W2006101334 date "2009-01-01" @default.
- W2006101334 modified "2023-10-18" @default.
- W2006101334 title "Lyapunov Function and Local Feedback Boundary Stabilization of the Navier–Stokes Equations" @default.
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- W2006101334 doi "https://doi.org/10.1137/070682630" @default.
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