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Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes system in 2D
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LONGTIME BEHAVIOR FOR A MODEL OF HOMOGENEOUS INCOMPRESSIBLE TWO-PHASE FLOWS
We consider a diffuse interface model for the evolution of an iso-thermal incompressible two-phase flow in a two-dimensional bounded domain. The model consists of the Navier-Stokes equation for the…
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Global existence of weak solutions to a nonlocal Cahn–Hilliard–Navier–Stokes system
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On Nonlocal Cahn–Hilliard–Navier–Stokes Systems in Two Dimensions
TLDR
The uniqueness technique can be adapted to show the validity of a smoothing property for the difference of two trajectories which is crucial to establish the existence of an exponential attractor and the latter is established even in the case of variable viscosity, constant mobility and regular potential.
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Uniform attractors of nonautonomous dynamical systems with memory
The study of nonlinear dynamical systems is of basic importance in the understanding of several natural phenomena. If a certain mathematical model is described by a nonlinear dynamical system, then…
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Strong solutions for two-dimensional nonlocal Cahn–Hilliard–Navier–Stokes systems
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The Cahn–Hilliard–Oono equation with singular potential
We consider the so-called Cahn–Hilliard–Oono equation with singular (e.g. logarithmic) potential in a bounded domain of ℝd, d ≤ 3. The equation is subject to an initial condition and Neumann…
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On a diffuse interface model of tumour growth
We consider a diffuse interface model of tumour growth proposed by A. Hawkins-Daruud et al. ((2013) J. Math. Biol.67 1457–1485). This model consists of the Cahn–Hilliard equation for the tumour cell…
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On the Cahn–Hilliard–Brinkman system
We consider a diffuse interface model for phase separation of an isothermal incompressible binary fluid in a Brinkman porous medium. The coupled system consists of a convective Cahn-Hilliard equation…
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Cahn–Hilliard–Navier–Stokes systems with moving contact lines
We consider a well-known diffuse interface model for the study of the evolution of an incompressible binary fluid flow in a two or three-dimensional bounded domain. This model consists of a system of…
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