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Zbl 1106.93011
Guerrero, Sergio
Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions. (English)
[J] ESAIM, Control Optim. Calc. Var. 12, 484-544 (2006). ISSN 1292-8119; ISSN 1262-3377/e

Summary: In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time $T>0$. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

MSC 2000:: *93B05 Controllability
35Q30 Stokes and Navier-Stokes equations
49J20 Optimal control problems with PDE (existence)
93C10 Nonlinear control systems

Keywords: Navier-Stokes system; controllability; slip

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