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Control problems for the Navier-Stokes system with nonlocal spatial terms

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 complicated 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.
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Dates and versions

hal-03819799 , version 1 (18-10-2022)

Identifiers

  • HAL Id : hal-03819799 , version 1

Cite

Nicolás Carreño, Takéo Takahashi. Control problems for the Navier-Stokes system with nonlocal spatial terms. 2022. ⟨hal-03819799⟩
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