Boundary stabilisation of the Navier-Stokes equation with fading memory. (English) Zbl 1328.93207
Summary: In this paper, it is studied the stabilisability problem of the Navier-Stokes system with memory, by boundary Dirichlet feedback controllers. Based on the spectral properties of the Oseen-Stokes operator, it is designed a stabilising finite-dimensional feedback controller that acts oblique on the boundary.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93C20 | Control/observation systems governed by partial differential equations |
| 35Q93 | PDEs in connection with control and optimization |
| 35Q30 | Navier-Stokes equations |
| 76D07 | Stokes and related (Oseen, etc.) flows |
| 76D55 | Flow control and optimization for incompressible viscous fluids |
| 34K20 | Stability theory of functional-differential equations |
Keywords:
Navier-Stokes equation with memory; viscoelastic fluids; Oseen-Stokes operator; feedback control; eigenvalue; dafermos methodReferences:
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