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We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…

Analysis of PDEs · Mathematics 2022-05-17 Sebastian Hensel , Yuning Liu

We discuss the sharp interface limit of a coupled Navier-Stokes/Allen-Cahn system in a two dimensional, bounded and smooth domain, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero…

Analysis of PDEs · Mathematics 2023-03-09 Helmut Abels , Mingwen Fei

We perform a rigorous examination of the sharp interface limit of a coupled Navier-Stokes and mass-conserving Allen-Cahn system in a two-dimensional, bounded, and smooth domain as the parameter $\varepsilon > 0$, representing the thickness…

Analysis of PDEs · Mathematics 2026-04-14 Helmut Abels , Hanifah Mumtaz

We are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper. When the thickness of the diffuse interfacial zone, which is parameterized by $\varepsilon$, goes to zero, we…

Analysis of PDEs · Mathematics 2022-05-04 Song Jiang , Xiangxiang Su , Feng Xie

We consider a two-phase flow of two incompressible, viscous and immiscible fluids which are separated by a sharp interface in the case of a simple phase transition. In this model the interface is no longer material and its evolution is…

Analysis of PDEs · Mathematics 2017-06-01 Helmut Abels , Maximilian Moser

We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility $m_\varepsilon=\sqrt{\varepsilon}$, where the small parameter $\varepsilon>0$…

Analysis of PDEs · Mathematics 2023-04-28 Helmut Abels , Mingwen Fei , Maximilian Moser

In this paper, we propose and analyze a diffuse interface model for inductionless magnetohydrodynamic fluids. The model couples a convective Cahn-Hilliard equation for the evolution of the interface, the Navier-Stokes system for fluid flow…

Analysis of PDEs · Mathematics 2023-12-20 Xiaodi Zhang

This paper concerns the sharp interface limit of solutions to the inhomogeneous incompressible Navier-Stokes/Allen-Cahn coupled system in a bounded domain $\Omega \subset \mathbb{R}^n,\ n =2,3$. Based on a relative energy method, we prove…

Analysis of PDEs · Mathematics 2023-05-18 Song Jiang , Xiangxiang Su , Feng Xie

A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…

Analysis of PDEs · Mathematics 2014-11-13 Wolfgang Dreyer , Jan Giesselmann , Christiane Kraus

In this paper, we study the large time behavior and sharp interface limit of the Cauchy problem for compressible Navier-Stokes/Allen-Cahn system with interaction shock waves in the same family. This system is an important mathematical model…

Analysis of PDEs · Mathematics 2024-06-05 Yazhou Chen , Qiaolin He , Xiaoding Shi , Xiaoping Wang

This paper is concerned with the incompressible limit problem for strong solutions of compressible two-phase flow models under periodic boundary conditions, where the Navier-Stokes equations are nonlinearly coupled with either Cahn-Hilliard…

Analysis of PDEs · Mathematics 2025-03-04 Yinghua Li , Manrou Xie

The sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact line problem are studied by asymptotic analysis and numerical simulations. The effects of the {mobility} number as well…

Analysis of PDEs · Mathematics 2019-11-12 Xianmin Xu , Yana Di , Haijun Yu

In this paper, we study a diffuse interface model for two-phase immiscible flows coupled by Navier-Stokes equations and mass-conserving Allen-Cahn equations. The contact line (the intersection of the fluid-fluid interface with the solid…

Analysis of PDEs · Mathematics 2025-03-12 Yinghua Li , Yuanxiang Yan , Xijun Yin

In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math.,…

Analysis of PDEs · Mathematics 2022-10-19 Yazhou Chen , Yi Peng , Qiaolin He , Xiaoding Shi

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

We consider the sharp interface limit of a convective Allen-Cahn equation, which can be part of a Navier-Stokes/Allen-Cahn system, for different scalings of the mobility $m_\varepsilon=m_0\varepsilon^\theta$ as $\varepsilon\to 0$. In the…

Analysis of PDEs · Mathematics 2021-02-22 Helmut Abels

In this letter, we derive the sharp-interface limit of the Cahn-Hilliard-Biot equations using formal matched asymptotic expansions. We find that in each sub-domain, the quasi-static Biot equations are obtained with domain-specific material…

Analysis of PDEs · Mathematics 2024-12-06 Erlend Storvik , Carina Bringedal

We consider the sharp interface limit of a coupled Stokes/Allen-Cahn system, when a parameter $\varepsilon>0$ that is proportional to the thickness of the diffuse interface tends to zero, in a two dimensional bounded domain. For…

Analysis of PDEs · Mathematics 2017-01-04 Helmut Abels , YuNing Liu

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase field approach is…

Analysis of PDEs · Mathematics 2019-12-20 Christian Rohde , Lars von Wolff

We show convergence of the Navier-Stokes/Allen-Cahn system to a classical sharp interface model for the two-phase flow of two viscous incompressible fluids with same viscosities in a smooth bounded domain in two and three space dimensions…

Analysis of PDEs · Mathematics 2024-06-06 Helmut Abels , Julian Fischer , Maximilian Moser
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