scholarly journals The second grade fluid and averaged Euler equations with Navier-slip boundary conditions

Nonlinearity ◽  
2003 ◽  
Vol 16 (3) ◽  
pp. 1119-1149 ◽  
Author(s):  
Adriana Valentina Busuioc ◽  
Tudor S Ratiu
Keyword(s):  
Boundary Conditions ◽  
Euler Equations ◽  
Second Grade ◽  
Slip Boundary Conditions ◽  
Second Grade Fluid ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions ◽  
Grade Fluid

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

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
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 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.

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