Related papers: Optimal boundary control for the Cahn-Hilliard-Nav…
We investigate the role of interfaces as transport barriers in binary-fluid turbulence by employing Lagrangian tracer particles. The Cahn-Hilliard-Navier-Stokes (CHNS) system of partial differential equations provides a natural theoretical…
The Cahn-Hilliard-Navier-Stokes (CHNS) system utilizes a diffusive phase-field for interface tracking of multi-phase fluid flows. Recently structure preserving methods for CHNS have moved into focus to construct numerical schemes that, for…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed…
We analyze a bilinear optimal control problem for the Stokes--Brinkman equations: the control variable enters the state equations as a coefficient. In two- and three-dimensional Lipschitz domains, we perform a complete continuous analysis…
We consider the Navier-Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and…
We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…
This paper focuses on the stability of solutions for a velocity-tracking problem associated with the two-dimensional Navier-Stokes equations. The considered optimal control problem does not possess any regularizer in the cost, and hence…
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…
In this paper, we investigate the global solvability of the chemotaxis-Navier-Stokes system on a three-dimensional moving domain of finite depth, bounded below by a rigid flat bottom and bounded above by the free surface. Completing the…
Nonlinear convection, the source of turbulence in fluid flows, may hold the key to stabilizing turbulence by solving a specific cubic polynomial equation. We consider the incompressible Navier-Stokes equations in a two-dimensional channel.…
In the recent paper `Well-posedness and regularity for a generalized fractional Cahn-Hilliard system' (arXiv:1804.11290) by the same authors, general well-posedness results have been established for a a class of evolutionary systems of two…
We consider the 2D incompressible Navier-Stokes equation in a rectangle with the usual no-slip boundary condition prescribed on the upper and lower boundaries. We prove that for any positive time, for any finite energy initial data, there…
In this paper, we deal with the existence of insensitizing controls for the Navier-Stokes equations in a bounded domain with Dirichlet boundary conditions. We prove that there exist controls insensitizing the $L^2$ -norm of the observation…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an…
We analyze the state constrained inverse Stefan type parabolic free boundary problem as an optimal control problem in the Sobolev-Besov spaces framework. Boundary heat flux, density of heat sources, and free boundary are components of the…
This paper concerns the global well posedness issue of the Navier-Stokes equations (CNS) describing barotropic compressible fluid flow with free surface occupied in the three dimensional exterior domain. Combining the maximal $L_p$-$L_q$…
In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis based on minimal assumptions on data and domain. We show the…
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the $L^2$ norm and an energy space seminorm. We prove well-posedness and…