English
Related papers

Related papers: Nonlocal Cahn-Hilliard-Navier-Stokes systems with …

200 papers

This paper is mainly concerned with an initial-boundary value problem of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with the Landau potential in a two and three dimensions. The existence of strong solutions with…

Analysis of PDEs · Mathematics 2025-09-22 Lingxin Jiang , Jiahong Wu , Fuyi Xu

A nonlocal Cahn-Hilliard model with a nonsmooth potential of double-well obstacle type that promotes sharp interfaces in the solution is presented. To capture long-range interactions between particles, a nonlocal Ginzburg-Landau energy…

Analysis of PDEs · Mathematics 2021-09-13 Olena Burkovska , Max Gunzburger

We study the well-posedness of a coupled Cahn-Hilliard-Stokes-Darcy system which is a diffuse-interface model for essentially immiscible two phase incompressible flows with matched density in a karstic geometry. Existence of finite energy…

Analysis of PDEs · Mathematics 2014-05-22 Daozhi Han , Xiaoming Wang , Hao WU

We prove convergence of suitable subsequences of weak solutions of a diffuse interface model for the two-phase flow of incompressible fluids with different densities with a nonlocal Cahn-Hilliard equation to weak solutions of the…

Analysis of PDEs · Mathematics 2022-01-19 Helmut Abels , Yutaka Terasawa

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…

Analysis of PDEs · Mathematics 2026-01-13 Andrea Giorgini , Jingning He , Hao Wu

In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is…

Analysis of PDEs · Mathematics 2024-11-12 Shijin Ding , Yinghua Li , Zhilin Lin , Yuanxiang Yan

In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in $3D$ domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the…

Analysis of PDEs · Mathematics 2017-10-10 Blanca Climent-Ezquerra , Francisco Guillén-González

The full compressible Navier-Stokes system describing the motion of a viscous, compressible, heat-conductive, and Newtonian polytropic fluid is studied in a three-dimensional simply connected bounded domain with smooth boundary having a…

Analysis of PDEs · Mathematics 2022-07-04 Jing Li , Boqiang Lü , Xue Wang

We consider weak solutions for a diffuse interface model of two non-Newtonian viscous, incompressible fluids of power-law type in the case of different densities in a bounded, sufficiently smooth domain. This leads to a coupled system of a…

Analysis of PDEs · Mathematics 2017-01-03 Helmut Abels , Dominic Breit

We obtain the existence and the structure of the weak uniform (with respect to the initial time) global attractor and construct a trajectory attractor for the 3D Navier-Stokes equations (NSE) with a fixed time-dependent force satisfying a…

Dynamical Systems · Mathematics 2023-05-09 Alexey Cheskidov , Songsong Lu

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…

Analysis of PDEs · Mathematics 2025-12-30 Andrea Giorgini , Jingning He , Hao Wu

In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak…

We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one…

Analysis of PDEs · Mathematics 2025-02-12 Charles M. Elliott , Thomas Sales

We study a nonlocal variant of a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. The model is described by a Navier--Stokes--Cahn--Hilliard system that…

Analysis of PDEs · Mathematics 2025-12-15 Kin Shing Chan , Kei Fong Lam

This paper would focus on the subject of the 2-D incompressible Navier-Stokes-Cahn-Hilliard (NS-CH) system with a singular free energy density. Due to lack of the maximum principle for the convective Cahn-Hilliard equation (as a…

Analysis of PDEs · Mathematics 2018-11-19 Guilong Gui , Zhenbang Li

We examine a viscous Cahn-Hilliard phase-separation model with memory and where the chemical potential possesses a nonlocal fractional Laplacian operator. The existence of global weak solutions is proven using a Galerkin approximation…

Analysis of PDEs · Mathematics 2018-05-01 Eylem Öztürk , Joseph L. Shomberg

We consider a phase-field model where the internal energy depends on the order parameter in a nonlocal way. Therefore, the resulting system consists of the energy balance equation coupled with a nonlinear and nonlocal ODE for the order…

Analysis of PDEs · Mathematics 2011-10-27 Maurizio Grasselli , Giulio Schimperna

We analyze the pressureless Navier-Stokes system with nonlocal attraction-repulsion forces. Such systems appear in the context of models of collective behavior. We prove the existence of weak solutions on the whole space $\mathbb{R}^3$ in…

Analysis of PDEs · Mathematics 2024-02-19 Piotr B. Mucha , Maja Szlenk , Ewelina Zatorska

A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…

Analysis of PDEs · Mathematics 2020-07-28 Zhilei Liang , Dehua Wang

We investigate the nonlocal version of the Abels-Garcke-Gr\"{u}n (AGG) system, which describes the motion of a mixture of two viscous incompressible fluids. This consists of the incompressible Navier-Stokes-Cahn-Hilliard system…

Analysis of PDEs · Mathematics 2022-12-08 Ciprian G. Gal , Andrea Giorgini , Maurizio Grasselli , Andrea Poiatti