518 research outputs found
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
We study a diffuse interface model for incompressible isothermal mixtures of
two immiscible fluids coupling the Navier--Stokes system with a convective
nonlocal Cahn--Hilliard equation in two dimensions of space. We apply recently
proved well-posedness and regularity results in order to establish existence of
optimal controls as well as first-order necessary optimality conditions for an
associated optimal control problem in which a distributed control is applied to
the fluid flow.Comment: 32 page
On a non-isothermal diffuse interface model for two-phase flows of incompressible fluids
We introduce a diffuse interface model describing the evolution of a mixture
of two different viscous incompressible fluids of equal density. The main
novelty of the present contribution consists in the fact that the effects of
temperature on the flow are taken into account. In the mathematical model, the
evolution of the macroscopic velocity is ruled by the Navier-Stokes system with
temperature-dependent viscosity, while the order parameter representing the
concentration of one of the components of the fluid is assumed to satisfy a
convective Cahn-Hilliard equation. The effects of the temperature are
prescribed by a suitable form of the heat equation. However, due to quadratic
forcing terms, this equation is replaced, in the weak formulation, by an
equality representing energy conservation complemented with a differential
inequality describing production of entropy. The main advantage of introducing
this notion of solution is that, while the thermodynamical consistency is
preserved, at the same time the energy-entropy formulation is more tractable
mathematically. Indeed, global-in-time existence for the initial-boundary value
problem associated to the weak formulation of the model is proved by deriving
suitable a-priori estimates and showing weak sequential stability of families
of approximating solutions.Comment: 26 page
Optimal distributed control of a nonlocal Cahn-Hilliard/Navier-Stokes system in 2D
We study a diffuse interface model for incompressible isothermal
mixtures of two immiscible fluids coupling the Navier-Stokes system with a
convective nonlocal Cahn-Hilliard equation in two dimensions of space. We
apply recently proved well-posedness and regularity results in order to
establish existence of optimal controls as well as first-order necessary
optimality conditions for an associated optimal control problem in which a
distributed control is applied to the fluid flow
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