scholarly journals Numerical aproximation of an optimal control problem associated with the Navier-Stokes equations

1989 ◽  
Vol 2 (1) ◽  
pp. 29-31 ◽  
Author(s):  
Max D. Gunzburger ◽  
LiSheng Hou ◽  
Thomas P. Svobodny
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn–Hilliard–Navier–Stokes equations

Analysis ◽  
2020 ◽  
Vol 40 (3) ◽  
pp. 127-150
Author(s):  
Tania Biswas ◽  
Sheetal Dharmatti ◽  
Manil T. Mohan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Minimum Principle ◽  
Immiscible Fluids ◽  
Second Order ◽  
Navier Stokes ◽  
Distributed Optimal Control ◽  
Navier Stokes Equations

AbstractIn this paper, we formulate a distributed optimal control problem related to the evolution of two isothermal, incompressible, immiscible fluids in a two-dimensional bounded domain. The distributed optimal control problem is framed as the minimization of a suitable cost functional subject to the controlled nonlocal Cahn–Hilliard–Navier–Stokes equations. We describe the first order necessary conditions of optimality via the Pontryagin minimum principle and prove second order necessary and sufficient conditions of optimality for the problem.

Numerical resolution of optimal control problem for the in-stationary Navier–Stokes equations

2019 ◽  
Vol 27 (1) ◽  
pp. 43-52
Author(s):  
Jamil Satouri
Keyword(s):  
Optimal Control ◽  
Finite Elements ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stokes Equations ◽  
Explicit Scheme ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Resolution ◽  
Stationary Navier Stokes Equations

Abstract In this paper we present a study of optimal control problem for the unsteady Navier–Stokes equations. We discuss the existence of the solution, adopt a new numerical resolution for this problem and combine Euler explicit scheme in time and both of methods spectral and finite elements in space. Finally, we give some numerical results proving the effectiveness of our approach.

scholarly journals Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sultana Ben Aadi ◽  
Khalid Akhlil ◽  
Khadija Aayadi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Fractional Derivative ◽  
Weak Solutions ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Galerkin Approximation ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Fractional Derivative

Abstract In this paper, we introduce the g-Navier–Stokes equations with time-fractional derivative of order α ∈ ( 0 , 1 ) {\alpha\in(0,1)} in domains of ℝ 2 {\mathbb{R}^{2}} . We then study the existence and uniqueness of weak solutions by means of the Galerkin approximation. Finally, an optimal control problem is considered and solved.

Optimal control of a coefficient in modification Navier-Stokes equations

2010 ◽  
Vol 60 (1) ◽  
Author(s):  
Nataša Bilić
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Kinematic Viscosity ◽  
Stokes Equations ◽  
Control Variable ◽  
Positive Function ◽  
Navier Stokes ◽  
Existence Of A Solution ◽  
Navier Stokes Equations ◽  
Finite Dimensional

AbstractThis paper deals with the optimal control of a coefficient in the modification of Navier-Stokes equations. Namely, the motion of the viscous incompressible fluid for a small gradient of velocity is described by Navier-Stokes equations where the coefficient of the kinematic viscosity ν is the positive constant (ν 0). For a greater gradient of velocity the coefficient of kinematic viscosity is a positive function of the gradient of velocity, that is ν (|∇u|). In our case ν (|∇u|) = ν 0 + ν 1 a (|∇u|) where ν 0, ν 1 ∈ ℝ+. The function a is positive and monotone and it is taken as a control variable. The existence of a solution of the optimal control problem is proved. Further, the approximation of the control problem by the finite-dimensional control problem is performed. The proof of the existence of a solution of that aproximate problem has been brought into light. Finally, the connection between the solution of the control problem and the solution of the approximate control problem is established.

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