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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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915609166479360 |
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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 |
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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 |