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This paper concerns a diffuse interface model for the flow of two incompressible viscoelastic fluids in a bounded domain. More specifically, the fluids are assumed to be macroscopically immiscible, but with a small transition region, where…

Analysis of PDEs · Mathematics 2024-11-15 Yadong Liu , Dennis Trautwein

We propose a new class of phase field models coupled to viscoelasticity with large deformations, obtained from a diffuse interface mixture model composed by a phase with elastic properties and a liquid phase. The model is formulated in the…

Analysis of PDEs · Mathematics 2022-04-12 Abramo Agosti , Pierluigi Colli , Harald Garcke , Elisabetta Rocca

We consider a fluid model including viscoelastic and viscoplastic effects. The state is given by the fluid velocity and an internal stress tensor that is transported along the flow with the Zaremba-Jaumann derivative. Moreover, the stress…

Analysis of PDEs · Mathematics 2022-02-11 Thomas Eiter , Katharina Hopf , Alexander Mielke

We study a quasi-incompressible Navier--Stokes/Cahn--Hilliard coupled system which describes the motion of two macroscopically immiscible incompressible viscous fluids with partial mixing in a small interfacial region and long-range…

Analysis of PDEs · Mathematics 2025-08-12 Mingwen Fei , Xiang Fei , Daozhi Han , Yadong Liu

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…

Analysis of PDEs · Mathematics 2024-06-03 Jingning He , Hao Wu

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…

Analysis of PDEs · Mathematics 2023-07-28 Andrea Di Primio , Maurizio Grasselli , Hao Wu

In [Cheng, Lasarzik, Thomas 2025 ARXIV-Preprint 2509.25508], we studied a Cahn--Hilliard two-phase model describing the flow of two viscoelastoplastic fluids in the framework of dissipative solutions using a logarithmic potential for the…

Analysis of PDEs · Mathematics 2026-01-14 Fan Cheng , Robert Lasarzik , Marita Thomas

While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…

We propose a new Cahn-Hilliard phase field model coupled to incompressible viscoelasticity at large strains, obtained from a diffuse interface mixture model and formulated in the Eulerian configuration. A new kind of diffusive…

Analysis of PDEs · Mathematics 2023-01-23 Abramo Agosti , Pierluigi Colli , Harald Garcke , Elisabetta Rocca

We introduce a new phase field model for tumour growth where viscoelastic effects are taken into account. The model is derived from basic thermodynamical principles and consists of a convected Cahn--Hilliard equation with source terms for…

Numerical Analysis · Mathematics 2024-06-21 Harald Garcke , Balázs Kovács , Dennis Trautwein

We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…

Analysis of PDEs · Mathematics 2024-08-15 Helmut Abels , Harald Garcke , Andrea Poiatti

We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…

Analysis of PDEs · Mathematics 2023-12-22 Thomas Eiter , Katharina Hopf , Robert Lasarzik

We show short-time well-posedness of a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2026-05-01 Helmut Abels , Jonas Haselböck

The formal sharp-interface asymptotics in a degenerate Cahn-Hilliard model for viscoelastic phase separation with cross-diffusive coupling to a bulk stress variable are shown to lead to non-local lower-order counterparts of the classical…

Analysis of PDEs · Mathematics 2026-05-22 Katharina Hopf , John King , Andreas Münch , Barbara Wagner

We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…

Analysis of PDEs · Mathematics 2025-09-15 Pierluigi Colli , Patrik Knopf , Giulio Schimperna , Andrea Signori

We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter…

Soft Condensed Matter · Physics 2009-11-10 Tatsuhiro Imaeda , Akira Furukawa , Akira Onuki

We prove existence of weak solutions to a diffuse interface model describing the flow of a fluid through a deformable porous medium consisting of two phases. The system non-linearly couples Biot's equations for poroelasticity, including…

Analysis of PDEs · Mathematics 2024-08-27 Helmut Abels , Harald Garcke , Jonas Haselböck

We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…

Analysis of PDEs · Mathematics 2023-10-25 Andrea Giorgini , Patrik Knopf

This article is concerned with a gradient-flow approach to a Cahn-Hilliard model for viscoelastic phase separation introduced by Zhou et al. (Phys. Rev. E, 2006) in its variant with constant mobility. By means of time-incremental…

Analysis of PDEs · Mathematics 2025-08-22 Moritz Immanuel Gau , Katharina Hopf

In this paper, we consider a stochastic version of the Cahn-Hilliard-Brinkman model in a smooth two- or three-dimensional domain with dynamical boundary conditions. The system describes creeping two-phase flows and is basically a coupling…

Probability · Mathematics 2026-01-13 Z. Brzeźniak , A. Ndongmo Ngana , T. Tachim Medjo
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