Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions

  • Duy Phan
  • Sérgio S. Rodrigues


The 3D Navier–Stokes system, under Lions boundary conditions, is proven to be approximately controllable provided a suitable saturating set does exist. An explicit saturating set for 3D rectangles is given.


Navier–Stokes equations Approximate controllability Saturating set 

Mathematics Subject Classification (2010)

93B05 35Q30 93C20 



The authors acknowledge partial support from the Austrian Science Fund (FWF): P 26034-N25. D. Phan also acknowledges partial support from the foundation of Tampere University of Technology, and thanks RICAM-ÖAW, Linz, where most of the work has been done, for the provided support and hospitality. The authors are also grateful to the anonymous referee for their constructive comments and suggestions, which have helped the authors to improve the exposition and the presentation of the results in the paper.


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Authors and Affiliations

  1. 1.Mathematics LaboratoryTampere University of TechnologyTampereFinland
  2. 2.Johann Radon Institute for Computational and Applied MathematicsÖAWLinzAustria

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