Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exis...

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Bibliographic Details
Published inAsymptotic analysis Vol. 126; no. 3-4; pp. 379 - 399
Main Authors Gariboldi, Claudia, Takahashi, Takéo
Format Journal Article
LanguageEnglish
Published Amsterdam IOS Press BV 01.01.2022
IOS Press
Subjects
Analysis of PDEs
Asymptotic properties
Boundary conditions
Coefficient of friction
Control systems
Convergence
Dirichlet problem
Fluid flow
Fluid mechanics
Incompressible flow
Incompressible fluids
Mathematics
Mechanics
Navier-Stokes equations
Optimal control
Optimization and Control
Physics
Slip
Navier slip boundary condition
optimal control
Navier-Stokes system
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Summary:We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.
ISSN:0921-7134
1875-8576
DOI:10.3233/ASY-211685