Well-posedness of Strong Solutions for a Thermodynamically Consistent Diffuse-interface Model for Incompressible Two-phase Flows with a Soluble Surfactant
Abstract
We consider a thermodynamically consistent diffuse-interface model for binary mixtures of incompressible viscous Newtonian fluids with a soluble surfactant. This hydrodynamic system generalizes the Abels-Garcke-Grün model for two-phase flows with unmatched densities by incorporating an additional Cahn-Hilliard equation for the surfactant concentration. We study the strong well-posedness of the initial-boundary value problem with physically relevant singular potentials, subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the corresponding chemical potentials. First, we establish the existence of local-in-time strong solutions in three dimensions and global-in-time strong solutions in two dimensions. In the two-dimensional case, we further show that, under natural growth assumptions on the singular potentials, strong solutions remain strictly separated from the pure phases, thereby guaranteeing uniqueness. In the three-dimensional case, we establish local-in-time uniqueness of strong solutions, provided that the initial data are strictly separated from the pure phases. Our results extend previous work on strong solutions to the Abels-Garcke-Grün model from the special case of constant mobility to the more general scenario with concentration-dependent mobilities and interactions with a surfactant.
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BibTeX
@misc{grasselli2026wellposedness,
title = {{Well-posedness of Strong Solutions for a Thermodynamically Consistent Diffuse-interface Model for Incompressible Two-phase Flows with a Soluble Surfactant}},
author = {Maurizio Grasselli and Bohan Ouyang and Hao Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10009},
eprint = {2610.10009},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10009},
}
RIS
TY - UNPB
TI - Well-posedness of Strong Solutions for a Thermodynamically Consistent Diffuse-interface Model for Incompressible Two-phase Flows with a Soluble Surfactant
AU - Maurizio Grasselli
AU - Bohan Ouyang
AU - Hao Wu
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10009
UR - https://arxiv.org/abs/2610.10009
AB - We consider a thermodynamically consistent diffuse-interface model for binary mixtures of incompressible viscous Newtonian fluids with a soluble surfactant. This hydrodynamic system generalizes the Abels-Garcke-Grün model for two-phase flows with unmatched densities by incorporating an additional Cahn-Hilliard equation for the surfactant concentration. We study the strong well-posedness of the initial-boundary value problem with physically relevant singular potentials, subject to a no-slip boundary condition for the fluid velocity and homogeneous Neumann boundary conditions for the phase-field variables and the corresponding chemical potentials. First, we establish the existence of local-in-time strong solutions in three dimensions and global-in-time strong solutions in two dimensions. In the two-dimensional case, we further show that, under natural growth assumptions on the singular potentials, strong solutions remain strictly separated from the pure phases, thereby guaranteeing uniqueness. In the three-dimensional case, we establish local-in-time uniqueness of strong solutions, provided that the initial data are strictly separated from the pure phases. Our results extend previous work on strong solutions to the Abels-Garcke-Grün model from the special case of constant mobility to the more general scenario with concentration-dependent mobilities and interactions with a surfactant.
ER -