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Control Problems for the Navier–Stokes System with Nonlocal Spatial Terms

Author

Listed:
  • Nicolás Carreño

    (Universidad Técnica Federico Santa María)

  • Takéo Takahashi

    (Université de Lorraine)

Abstract

We consider the local null controllability of a modified Navier–Stokes system where we include nonlocal spatial terms. We generalize a previous work where the nonlocal spatial term is given by the linearization of a Ladyzhenskaya model for a viscous incompressible fluid. Here, the nonlocal spatial term is more general and we consider a control with one vanishing component. The proof of the result is based on a Carleman estimate where the main difficulty consists in handling the nonlocal spatial terms. One key point corresponds to a particular decomposition of the solution of the adjoint system that allows us to overcome regularity issues. With a similar approach, we also show the existence of insensitizing controls for the same system.

Suggested Citation

  • Nicolás Carreño & Takéo Takahashi, 2024. "Control Problems for the Navier–Stokes System with Nonlocal Spatial Terms," Journal of Optimization Theory and Applications, Springer, vol. 200(2), pages 724-767, February.
    • Handle: RePEc:spr:joptap:v:200:y:2024:i:2:d:10.1007_s10957-023-02321-1
    DOI: 10.1007/s10957-023-02321-1
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