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On the approximate and null controllability of the Navier-Stokes equations. (English) Zbl 0945.93017

This is a well-written survey article on the approximate and null controllability of the Navier-Stokes equations. The results discussed here are new and are accompanied by several open problems. Section 2 presents the work of Fabre based on a fixed-point argument. Section 3 is based on the results of Lions and Zuazua and discusses controllability results for finite-dimensional approximations. A “return” method of Coron is presented in Section 4. Finally, in Section 5 the author gives results on null controllability by Fursikov and Imanuvilov.
Reviewer: O.Cârjá (Iaşi)

MSC:

93C20 Control/observation systems governed by partial differential equations
76D05 Navier-Stokes equations for incompressible viscous fluids
93B05 Controllability
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