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

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Abstract

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.

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Acknowledgements

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. Mathematics Laboratory, Tampere University of Technology, P.O. Box 553, 33101, Tampere, Finland

    Duy Phan

  2. Johann Radon Institute for Computational and Applied Mathematics, ÖAW, Altenbergerstraße 69, 4040, Linz, Austria

    Sérgio S. Rodrigues

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  1. Duy Phan
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  2. Sérgio S. Rodrigues
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Correspondence to Duy Phan.

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Phan, D., Rodrigues, S.S. Approximate Controllability for Navier–Stokes Equations in 3D Rectangles Under Lions Boundary Conditions. J Dyn Control Syst 25, 351–376 (2019). https://doi.org/10.1007/s10883-018-9412-0

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  • DOI: https://doi.org/10.1007/s10883-018-9412-0

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