Stationary Cahn–Hilliard–Navier–Stokes equations for the diffuse interface model of compressible flows-Reference-Cited by-同舟云学术

Stationary Cahn–Hilliard–Navier–Stokes equations for the diffuse interface model of compressible flows

Published:2020-10-23 Issue:12 Volume:30 Page:2445-2486
ISSN:0218-2025
Container-title:Mathematical Models and Methods in Applied Sciences
language:en
Short-container-title:Math. Models Methods Appl. Sci.

Author:

Liang Zhilei¹,Wang Dehua²

Affiliation:

1. School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, P. R. China

2. Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Abstract

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 consist of the stationary Navier–Stokes equations for compressible fluids and a stationary Cahn–Hilliard type equation for the mass concentration difference. Approximate solutions are constructed through a two-level approximation procedure, and the limit of the sequence of approximate solutions is obtained by a weak convergence method. New ideas and estimates are developed to establish the existence of weak solutions with a wide range of adiabatic exponent.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modeling and Simulation

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218202520500475

Reference43 articles.

1. On a Diffuse Interface Model for Two-Phase Flows of Viscous, Incompressible Fluids with Matched Densities

2. Existence of Weak Solutions for a Diffuse Interface Model for Viscous, Incompressible Fluids with General Densities

3. Strong Well-posedness of a Diffuse Interface Model for a Viscous, Quasi-incompressible Two-phase Flow

4. Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

5. On a diffuse interface model for a two-phase flow of compressible viscous fluids

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