Global well-posedness of strong solutions to a bulk-surface Navier-Stokes-Cahn-Hilliard model with non-degenerate mobilities in two dimensions

2025/11/10 by Stange, Jonas
Engineering · Materials Science · Mathematics · #76D03 #76D05 #76D07 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Primary: 76T06 #Secondary: 35Q35 #Solidification and crystal growth phenomena

paper · doi:10.48550/arxiv.2511.06847

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

We examine a thermodynamically consistent diffuse interface model for bulk-surface viscous fluid mixtures. This model consists of a Navier--Stokes--Cahn--Hilliard model in the bulk coupled to a surface Navier--Stokes--Cahn--Hilliard system on the boundary. In this paper, we address the global well-posedness of strong solutions in the two-dimensional setting, also covering the physically meaningful case of non-degenerate mobility functions. Lastly, we prove the uniqueness of the corresponding strong solutions and their continuous dependence on the initial data. Our approach hinges upon new well-posedness and regularity theory for a convective bulk-surface Cahn--Hilliard equation with non-degenerate mobilities, as well as a bulk-surface Stokes equation with non-constant coefficients.

Citations

• A thermodynamically consistent model for bulk-surface viscous fluid mixtures: Model derivation and mathematical analysis
• Well-posedness and long-time behavior of a bulk-surface Cahn--Hilliard model with non-degenerate mobility
• Regularity of a bulk-surface Cahn-Hilliard model driven by Leray velocity fields
• On a phase field model for binary mixtures of micropolar fluids with non-matched densities and moving contact lines
• New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior
• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
• Separation property and asymptotic behavior for a transmission problem of the bulk-surface coupled Cahn-Hilliard system with singular potentials and its Robin approximation
• On the Cahn-Hilliard equation with kinetic rate dependent dynamic boundary condition and non-smooth potential: separation property and long-time behavior
• Two-phase flows through porous media described by a Cahn--Hilliard--Brinkman model with dynamic boundary conditions
• Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched 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

Related

• Strong solutions for two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems
• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
• Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
• Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
• On nonlocal Cahn-Hilliard-Navier-Stokes systems in two dimensions