Control Problems for the Navier–Stokes System with Nonlocal Spatial Terms
Journal of Optimization Theory and Applications(2024)
摘要
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.
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关键词
Navier–Stokes system,Controllability,Carleman estimates,Nonlocal spatial terms
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