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

Nicolás Carreño () and Takéo Takahashi ()
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Nicolás Carreño: Universidad Técnica Federico Santa María
Takéo Takahashi: Université de Lorraine

Journal of Optimization Theory and Applications, 2024, vol. 200, issue 2, No 11, 724-767

Abstract: 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.

Keywords: Navier–Stokes system; Controllability; Carleman estimates; Nonlocal spatial terms; 76D05; 93C20; 93B05; 93B07 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02321-1

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