Local well-posedness of a perturbation problem for the Abels-Garcke-Grün model in three dimensions

2025/06/19 by Lv, Maoyin
Engineering · Materials Science · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2506.16105

openalex publication_date 2025/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the Abels-Garcke-Grün model that describes the motion of two viscous incompressible fluids with unmatched densities in the presence of a uniform gravitational field. For the perturbated system with respect to a given equilibrium state in three dimensions, we establish the local existence and uniqueness of a strong solution using a suitable iteration scheme and the energy method. This work lays the foundation for further studies on the Rayleigh-Taylor instability problem of nonhomogeneous two-phase flows within the framework of diffuse interface models.

Citations

• Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
• A unified framework for Navier-Stokes Cahn-Hilliard models with non-matching densities
• Local Well-Posedness of a Quasi-Incompressible Two-Phase Flow
• Well-posedness of the two-dimensional Abels-Garcke-Grün model for two-phase flows with unmatched densities
• On Instability and Stability of Three-Dimensional Gravity Driven Viscous Flows in a Bounded Domain
• Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible Viscous Magnetohydrodynamic Flows
• On the Rayleigh-Taylor instability for incompressible viscous magnetohydrodynamic equations
• Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities
• Linear Rayleigh-Taylor instability for viscous, compressible fluids
• Compressible, inviscid Rayleigh-Taylor instability
• DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS

Related

• Well-posedness of the two-dimensional Abels-Garcke-Grün model for two-phase flows with unmatched densities
• Global well-posedness and convergence to equilibrium for the Abels-Garcke-Grün model with nonlocal free energy
• Existence and Stability of Strong Solutions to the Abels-Garcke-Gr "un\n model in Three Dimensions
• Well-posedness for a diffuse interface model of non-Newtonian two-phase flows
• Global existence of weak solutions for a nonlocal model for two-phase\n flows of incompressible fluids with unmatched densities