Related papers: Optimal distributed control of a nonlocal Cahn-Hil…
This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…
The convective Brinkman-Forchheimer (CBF) equations describe the motion of incompressible viscous fluid through a rigid, homogeneous, isotropic, porous medium. In this work, we consider some distributed optimal control problems like total…
In this paper, we consider an optimal control problem for the two-dimensional evolutionary Navier-Stokes system. Looking for sparsity, we take controls as functions of time taking values in a space of Borel measures. The cost functional…
We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approach for gradient systems and (rotational) pressure-correction…
In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving incompressible magnetic fluids with unmatched densities. The model couples the incompressible…
In this article, we study the control aspects of the one-dimensional compressible Navier-Stokes equations with Maxwell's law linearized around a constant steady state with zero velocity. We consider the linearized system with Dirichlet…
The purpose of this paper is to provide a large class of initial data which generates global smooth solution of the 3-D inhomogeneous incompressible Navier-Stokes system in the whole space~$\R^3$. This class of data is based on functions…
We study a diffuse-interface model for a binary incompressible mixture in a periodically perforated porous medium, described by a time-dependent Navier-Stokes-Cahn-Hilliard (NSCH) system posed on the pore domain…
This paper is concerned with the large time behavior of the Cauchy problem for Navier-Stokes/Allen-Cahn system describing the interface motion of immiscible two-phase flow in 3-D. The existence and uniqueness of global solutions and the…
In this article we study the local controllability of the one-dimensional Cahn-Hilliard-Navier-Stokes equation, that is Cahn-Hilliard-Burgers' equation, around a certain steady state using a localized interior control acting only in the…
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 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…
We analyze a fully discrete scheme based on the discontinuous (in time) Galerkin approach, which is combined with conforming finite element subspaces in space, for the distributed optimal control problem of the three-dimensional…
This paper investigates an optimal control problem associated with a two-dimensional multi-species Cahn-Hilliard-Keller-Segel tumor growth model, which incorporates complex biological processes such as species diffusion, chemotaxis,…
In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, are presented. We show that these inconsistencies are consequences of…
In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…
We study the motion of a compressible heat-conducting fluid in three dimensions interacting with a non-linear flexible shell. The fluid is described by the full Navier--Stokes--Fourier system. The shell constitutes an unknown part of the…
We consider a model describing the behavior of a mixture of two incompressible fluids with the same density in isothermal conditions. The model consists of three balance equations: continuity equation, Navier-Stokes equation for the mean…
In this paper, we study an optimal control problem for a viscous Cahn--Hilliard system with zero Neumann boundary conditions in which a hyperbolic relaxation term involving the second time derivative of the chemical potential has been added…
The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on the whole boundary. Our study is then…