[HTML][HTML] Global well-posedness and convergence to equilibrium for the Abels-Garcke-Grün model with nonlocal free energy

CG Gal, A Giorgini, M Grasselli, A Poiatti - Journal de Mathématiques Pures …, 2023 - Elsevier
We investigate the nonlocal version of the Abels-Garcke-Grün (AGG) system, which
describes the motion of a mixture of two viscous incompressible fluids. This consists of the …

Well-posedness of the two-dimensional Abels–Garcke–Grün model for two-phase flows with unmatched densities

A Giorgini - Calculus of Variations and Partial Differential …, 2021 - Springer
Abstract We study the Abels–Garcke–Grün (AGG) model for a mixture of two viscous
incompressible fluids with different densities. The AGG model consists of a Navier–Stokes …

Multi–component Cahn–Hilliard Systems with Singular Potentials: Theoretical Results

CG Gal, M Grasselli, A Poiatti, JL Shomberg - Applied Mathematics & …, 2023 - Springer
We consider a system of nonlinear diffusion equations modelling (isothermal) phase
segregation of an ideal mixture of N≥ 2 components occupying a bounded region Ω⊂ R d …

Existence and stability of strong solutions to the Abels–Garcke–Grün model in three dimensions

A Giorgini - Interfaces and Free Boundaries, 2022 - ems.press
Existence and stability of strong solutions to the Abels–Garcke–Grün model in three
dimensions Page 1 Interfaces Free Bound. 24 (2022), 565–608 DOI 10.4171/IFB/482 © 2022 …

New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior

M Conti, P Galimberti, S Gatti, A Giorgini - arXiv preprint arXiv:2410.22234, 2024 - arxiv.org
We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility
and logarithmic potential in two dimensions. We show that any weak solution is unique …

[HTML][HTML] A stochastic Allen–Cahn–Navier–Stokes system with singular potential

A Di Primio, M Grasselli, L Scarpa - Journal of Differential Equations, 2024 - Elsevier
We investigate a stochastic version of the Allen–Cahn–Navier–Stokes system in a smooth
two-or three-dimensional domain with random initial data. The system consists of a Navier …

Weak and very weak solutions to the viscous Cahn–Hilliard–Oberbeck–Boussinesq phase-field system on two-dimensional bounded domains

G Peralta - Journal of Evolution Equations, 2022 - Springer
In this paper, we consider weak and very weak solutions to the viscous Cahn–Hilliard–
Oberbeck–Boussinesq system for non-isothermal, viscous and incompressible binary fluid …

Exponential stability of a diffuse interface model of incompressible two-phase flow with phase variable dependent viscosity and vacuum

Y Li, M Xie, Y Yan - Journal of Differential Equations, 2025 - Elsevier
This paper is concerned with a simplified model for two-phase fluids with diffuse interface.
The model couples the nonhomogeneous incompressible Navier-Stokes equations with the …

Weak solution of a stochastic 3D nonlocal Cahn–Hilliard–Navier–Stokes systems with shear-dependent viscosity

A Ndongmo Ngana, G Deugoué, T Tachim Medjo - Stochastics, 2023 - Taylor & Francis
We consider the stochastic nonlocal Cahn–Hilliard–Navier–Stokes system with shear-
dependent viscosity on a bounded domain M⊂ R d, d= 2, 3, driven by a multiplicative noise …

On the rate of convergence of Yosida approximation for the nonlocal Cahn–Hilliard equation

P Gwiazda, J Skrzeczkowski… - IMA Journal of Numerical …, 2024 - academic.oup.com
It is well-known that one can construct solutions to the nonlocal Cahn–Hilliard equation with
singular potentials via Yosida approximation with parameter. The usual method is based on …