Phase Transition in Non-isentropic Compressible Immiscible Two-Phase Flow with van der Waals Equation of State

2025/06/26 by Yazhou Chen, Chen, Yazhou, Peng, Yi +4
Earth and Planetary Sciences · Engineering · Mathematics · #35B40 #35B65 #35C20 #35M10 #35Q35 #76N10 #76T30 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions #Particle Dynamics in Fluid Flows

paper · pdf · doi:10.48550/arxiv.2506.20955

openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

This study establishes the global well-posedness of the compressible non-isentropic Navier-Stokes/Allen-Cahn system governed by the van der Waals equation of state p(ρ,θ)=- aρ²+(Rθρ)/(1-bρ) and degenerate thermal conductivity κ(θ)=κθ^β, where p, ρ and θ are the pressure, the density and the temperature of the flow respectively, and a,b,R,κ are positive constants related to the physical properties of the flow. Navier-Stokes/Allen-Cahn system models immiscible two-phase flow with diffusive interfaces, where the non-monotonic pressure-density relationship in the van der Waals equation drives gas-liquid phase transitions. By developing a refined L²-energy framework, we prove the existence and uniqueness of global strong solutions to the one-dimensional Cauchy problem for non-vacuum and finite-temperature initial data, without imposing smallness restrictions on the initial conditions. The findings demonstrate that despite non-monotonic pressure inducing substantial density fluctuations and triggering phase transitions, all physical quantities remain bounded over finite time intervals.

Citations

• Strong Solutions for 1D Compressible Navier-Stokes/Allen-Cahn System with Phase Variable Dependent Viscosity
• Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System
• Global existence of strong solutions to the planar compressible magnetohydrodynamic equations with large initial data in unbounded domains
• The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity
• Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations

Related

• Global Solution for Gas-Liquid Flow of 1-D van der Waals Equation of State with Large Initial Data
• Global Strong Solution to a Thermodynamic Compressible Diffuse Interface Model with Temperature Dependent Heat-conductivity in 1-D
• The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity
• Diffuse planar phase boundaries in a two-phase fluid with one incompressible phase
• Stability of the Phase Separation State for Compressible Navier-Stokes/Allen-Cahn System