Local-in-time existence of strong solutions to a quasi-incompressible Cahn--Hilliard--Navier--Stokes system

TL;DR

This paper proves local-in-time existence and uniqueness of strong solutions for a quasi-incompressible two-phase flow model combining Cahn--Hilliard and Navier--Stokes equations, using fixed point and regularity theories.

Contribution

It establishes the first local existence and uniqueness results for a quasi-incompressible Cahn--Hilliard--Navier--Stokes system with unmatched densities.

Findings

Proved local existence and uniqueness of strong solutions.

Applied Banach fixed point theorem and maximal regularity theory.

Addressed a complex two-phase flow model with unmatched densities.

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.