Related papers: An optimal boundary control problem related to the…
We study some optimal control problems associated to the evolution of two isothermal, incompressible, immisible fluids in a two-dimensional bounded domain. The Cahn- Hilliard-Navier-Stokes model consists of a Navier-Stokes equation…
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…
This paper is devoted to the study of the turnpike phenomenon arising in the optimal distributed control tracking-type problem for the Navier-Stokes equations. We obtain a positive answer to this property in the case when the controls are…
In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence…
This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…
We deal with the 3D Navier-Stokes equation in a smooth simply connected bounded domain, with controls on a non-empty open part of the boundary and a Navier slip-with-friction boundary condition on the remaining, uncontrolled, part of the…
In 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…
In this paper we present a finite element analysis for a Dirichlet boundary control problem governed by the Stokes equation. The Dirichlet control is considered in a convex closed subset of the energy space $\mathbf{H}^1(\Omega).$ Most of…
A Pontryagin maximum principle for an optimal control problem in three dimensional linearized compressible viscous flows is established using the Ekeland variational principle. The controls are distributed over a bounded domain, while the…
Many problems in computational science and engineering are simultaneously characterized by the following challenging issues: uncertainty, nonlinearity, nonstationarity and high dimensionality. Existing numerical techniques for such models…
The aim of this paper is to investigate the existence of optimal controls for systems described by stochastic partial differential equations (SPDEs) with locally monotone coefficients controlled by different external forces which are…
In this paper we study the problem of energy conservation for the solutions of the initial boundary value problem associated to the 3D Navier-Stokes equations, with Dirichlet boundary conditions. First, we consider Leray-Hopf weak solutions…
In this proceeding we expose a particular case of a recent result obtained by the authors regarding the incompressible Navier-Stokes equations in a smooth bounded and simply connected bounded domain, either in 2D or in 3D, with a Navier…
The aim of this work is to study the optimal control problems of flows governed by the incompressible third grade fluid equations with Navier-slip boundary conditions. After recalling a result on the well-posedness of the state equations,…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
We consider the 2D incompressible Navier-Stokes equations with Dirichlet boundary condition in the exterior of one obstacle. Assuming that the circulation at infinity of the velocity is sufficiently small, we prove that the large time…
This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…