Fernández-Cara, Enrique On the approximate and null controllability of the Navier-Stokes equations. (English) Zbl 0945.93017 SIAM Rev. 41, No. 2, 269-277 (1999). 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) Cited in 5 Documents MSC: 93C20 Control/observation systems governed by partial differential equations 76D05 Navier-Stokes equations for incompressible viscous fluids 93B05 Controllability Keywords:approximate controllability; null controllability; Navier-Stokes equations; survey PDFBibTeX XMLCite \textit{E. Fernández-Cara}, SIAM Rev. 41, No. 2, 269--277 (1999; Zbl 0945.93017) Full Text: DOI