Normal feedback stabilization of periodic flows in a two-dimensional channel. (English) Zbl 1237.93153
Summary: We consider a two-dimensional incompressible channel flow with periodic condition along one axis. We stabilize the linearized system by a boundary feedback controller with vertical velocity observation, which acts on the normal component of the velocity only. The stability is achieved without any a-priori condition on the viscosity coefficient, that is, on the Reynolds number.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93C25 | Control/observation systems in abstract spaces |
| 35Q30 | Navier-Stokes equations |
| 93B52 | Feedback control |
Keywords:
Navier-Stokes equations; Fourier decomposition; analytic \(C _{0}\)-semigroups; feedback controllerReferences:
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