scholarly journals Optimal Control of the Two-Dimensional Stationary Navier--Stokes Equations with Measure Valued Controls

2019 ◽  
Vol 57 (2) ◽  
pp. 1328-1354 ◽  
Author(s):  
Eduardo Casas ◽  
Karl Kunisch
Keyword(s):  
Optimal Control ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
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.

On nonhomogeneous boundary value problems for the stationary Navier–Stokes equations in two-dimensional symmetric semi-infinite outlets

2015 ◽  
Vol 15 (04) ◽  
pp. 543-569 ◽  
Author(s):  
M. Chipot ◽  
K. Kaulakytė ◽  
K. Pileckas ◽  
W. Xue
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Domain Boundary ◽  
Boundary Value ◽  
Symmetric Domain ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Dirichlet Integral ◽  
Navier Stokes Equations ◽  
Stationary Navier Stokes Equations

We study the stationary nonhomogeneous Navier–Stokes problem in a two-dimensional symmetric domain with a semi-infinite outlet (for instance, either paraboloidal or channel-like). Under the symmetry assumptions on the domain, boundary value and external force, we prove the existence of at least one weak symmetric solution without any restriction on the size of the fluxes, i.e. the fluxes of the boundary value [Formula: see text] over the inner and the outer boundaries may be arbitrarily large. Only the necessary compatibility condition (the total flux is equal to zero) has to be satisfied. Moreover, the Dirichlet integral of the solution can be finite or infinite depending on the geometry of the domain.

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