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

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Auteur principal: Stange, Jonas
Format: Preprint
Publié: 2025
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author Stange, Jonas
author_facet Stange, Jonas
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2511_06847
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Global well-posedness of strong solutions to a bulk-surface Navier-Stokes-Cahn-Hilliard model with non-degenerate mobilities in two dimensions
Stange, Jonas
Analysis of PDEs
Mathematical Physics
Primary: 76T06, Secondary: 35Q35, 76D03, 76D05, 76D07
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.
title Global well-posedness of strong solutions to a bulk-surface Navier-Stokes-Cahn-Hilliard model with non-degenerate mobilities in two dimensions
topic Analysis of PDEs
Mathematical Physics
Primary: 76T06, Secondary: 35Q35, 76D03, 76D05, 76D07
url https://arxiv.org/abs/2511.06847