Existence of an Optimal Solution of a Shape Control Problem for the Stationary Navier--Stokes Equations

1998 ◽  
Vol 36 (3) ◽  
pp. 895-909 ◽  
Author(s):  
Max D. Gunzburger ◽  
Hongchul Kim
Keyword(s):  
Control Problem ◽  
Shape Control ◽  
Stokes Equations ◽  
Optimal Solution ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

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.

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.

Sign in / Sign up

Export Citation Format

Share Document