Related papers: Attractors for the Navier-Stokes-Cahn-Hilliard Sys…
We study a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effects. This model also takes into account some significant mechanisms such as active transport and nonlocal interactions of…
We analyze a Navier-Stokes-Cahn-Hilliard model for viscous incompressible two-phase flows where the mechanisms of chemotaxis, active transport and reaction are taken into account. The evolution system couples the Navier-Stokes equations for…
Here we consider a Cahn-Hilliard-Navier-Stokes system characterized by a nonlocal Cahn-Hilliard equation with a singular (e.g., logarithmic) potential. This system originates from a diffuse interface model for incompressible isothermal…
We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows with chemotaxis effect. The PDE system couples a Navier-Stokes equation for the fluid velocity, a convective Cahn-Hilliard equation for the…
In this paper, we mainly consider the long-time behavior of solutions for the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions and two polynomial growth nonlinearities of arbitrary order. We prove the existence of a…
The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal variant consists of the Navier-Stokes equations…
We consider a model for the evolution of a mixture of two incompressible and partially immiscible Newtonian fluids in two dimensional bounded domain. More precisely, we address the well-known model H consisting of the Navier-Stokes equation…
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard…
We analyze a diffuse interface model that describes the dynamics of incompressible two-phase flows influenced by interactions with a soluble chemical substance, encompassing the chemotaxis effect, mass transport, and reactions. In the…
We investigate a diffuse-interface model that describes the dynamics of incompressible two-phase viscous flows with surfactant. The resulting system of partial differential equations consists of a sixth-order Cahn-Hilliard equation for the…
We consider a 2D system that models the nematic liquid crystal flow through the Navier--Stokes equations suitably coupled with a transport-reaction-diffusion equation for the averaged molecular orientations. This system has been proposed as…
We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…
We consider a mathematical model coupling the Cahn-Hilliard system for phase separation with an additional equation describing the diffusion process of a chemical quantity whose concentration influences the physical process. The main…
We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…
We investigate a hydrodynamic system of Navier--Stokes/Cahn--Hilliard type, which describes the motion of a two-phase flow of two incompressible fluids with unmatched densities coupled with a soluble chemical species. Derived from Onsager's…
We study a Navier-Stokes/Cahn-Hilliard system modeling the evolution of a compressible binary mixture of viscous fluids undergoing phase separation. The novelty of this work is a free energy potential including the physically relevant…
We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable $\vp$, endowed with…
We study a diffuse-interface model that describes the dynamics of two-phase incompressible flows driven by the thermo-induced Marangoni effect. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity, the…
We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Existence of global weak and strong solutions under inhomogeneous…
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…