Local-in-Time Existence of Strong Solutions to a Quasi-Incompressible Cahn–Hilliard–Navier–Stokes System

Mingwen Fei; Xiang Fei; Daozhi Han; Yadong Liu

doi:10.1002/zamm.70443

Local-in-Time Existence of Strong Solutions to a Quasi-Incompressible Cahn–Hilliard–Navier–Stokes System

Mingwen Fei
, Xiang Fei
, Daozhi Han
, Yadong Liu

Mathematics

Anhui Normal University
Ministry of Education of the People's Republic of China

Research output: Contribution to journal › Article › peer-review

Abstract

We analyze a quasi-incompressible Cahn–Hilliard–Navier–Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.

Original language	English
Article number	e70443
Journal	ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Volume	106
Issue number	5
DOIs	https://doi.org/10.1002/zamm.70443
State	Published - May 2026

Keywords

Navier–Stokes–Cahn–Hilliard equations
diffuse interface model
free boundary value problems
quasi-incompressibility
two-phase flow

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10.1002/zamm.70443

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title = "Local-in-Time Existence of Strong Solutions to a Quasi-Incompressible Cahn{\textendash}Hilliard{\textendash}Navier{\textendash}Stokes System",

abstract = "We analyze a quasi-incompressible Cahn{\textendash}Hilliard{\textendash}Navier{\textendash}Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.",

keywords = "Navier{\textendash}Stokes{\textendash}Cahn{\textendash}Hilliard equations, diffuse interface model, free boundary value problems, quasi-incompressibility, two-phase flow",

author = "Mingwen Fei and Xiang Fei and Daozhi Han and Yadong Liu",

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T1 - Local-in-Time Existence of Strong Solutions to a Quasi-Incompressible Cahn–Hilliard–Navier–Stokes System

AU - Fei, Mingwen

AU - Fei, Xiang

AU - Han, Daozhi

AU - Liu, Yadong

PY - 2026/5

Y1 - 2026/5

N2 - We analyze a quasi-incompressible Cahn–Hilliard–Navier–Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.

AB - We analyze a quasi-incompressible Cahn–Hilliard–Navier–Stokes system (qCHNS) for two-phase flows with unmatched densities. The order parameter is the volume fraction difference of the two fluids, while mass-averaged velocity is adopted. This leads to a quasi-incompressible model where the pressure also enters the equation of the chemical potential. We establish local existence and uniqueness of strong solutions by the Banach fixed point theorem and the maximal regularity theory.

KW - Navier–Stokes–Cahn–Hilliard equations

KW - diffuse interface model

KW - free boundary value problems

KW - quasi-incompressibility

KW - two-phase flow

UR - https://www.scopus.com/pages/publications/105038043275

U2 - 10.1002/zamm.70443

DO - 10.1002/zamm.70443

M3 - Article

AN - SCOPUS:105038043275

SN - 0044-2267

VL - 106

JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

IS - 5

M1 - e70443

ER -

Local-in-Time Existence of Strong Solutions to a Quasi-Incompressible Cahn–Hilliard–Navier–Stokes System

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