Related papers: An Optimal Control Problem for the Navier--Stokes …
We study the incompressible stationary Navier-Stokes equations in the upper-half plane with homogeneous Dirichlet boundary condition and non-zero external forcing terms. Existence of weak solutions is proved under a suitable condition on…
In this paper, we study an optimal boundary control problem for the Boussinesq equations, which couple the time-dependent Navier-Stokes system with a heat equation, where the control enters through a Robin boundary condition on temperature.…
We consider randomly forced 2D Navier-Stokes equations in a bounded domain with smooth boundary. It is assumed that the random perturba- tion is non-degenerate, and its law is periodic in time and has a support localised with respect to…
In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
The approximation of the value function associated to a stabilization problem formulated as optimal control problem for the Navier-Stokes equations in dimension three by means of solutions to generalized Lyapunov equations is proposed and…
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the…
We develop a mathematical model for sailboat navigation that can play the same role that the Black and Scholes model plays in mathematical finance: it captures essential features of sailboat navigation, it can provide insights that might…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
Based on energy considerations, we derive a class of dynamic outflow boundary conditions for the incompressible Navier-Stokes equations, containing the well-known convective boundary condition but incorporating also the stress at the…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
We are concerned with the barotropic compressible Navier-Stokes system in a bounded domain of $\mathbb{R}^d$ (with $d\geq2$). In a critical regularity setting, we establish local well-posedness for large data with no vacuum and global…
The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
We consider the steady Navier-Stokes system with mixed boundary conditions, in subdomains of a holdall domain. We study, via the penalization method, its approximation properties. Error estimates, obtained using the extension operator,…
Considering channel flow at Reynolds numbers below the linear stability threshold of the laminar profile as a generic example system showing a subcritical transition to turbulence connected with the existence of simple invariant solutions,…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
A special class of optimal control problems with complementarity constraints on the control functions is studied. It is shown that such problems possess optimal solutions whenever the underlying control space is a first-order Sobolev space.…