Navier-Stokes-Cahn-Hilliard equations on evolving surfaces
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929708072960000 |
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| author | Elliott, Charles M. Sales, Thomas |
| author_facet | Elliott, Charles M. Sales, Thomas |
| contents | We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one prescribes the evolution of the surface. Well-posedness is proved for smooth potentials in the Cahn-Hilliard equation with polynomial growth, and also for a thermodynamically relevant singular potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Navier-Stokes-Cahn-Hilliard equations on evolving surfaces Elliott, Charles M. Sales, Thomas Analysis of PDEs 35K59 (Primary) 35Q35, 35K67 (Secondary) We derive a system of equations which can be seen as an evolving surface version of the diffuse interface "Model H" of Hohenberg and Halperin (1977). We then consider the well-posedness for the corresponding (tangential) system when one prescribes the evolution of the surface. Well-posedness is proved for smooth potentials in the Cahn-Hilliard equation with polynomial growth, and also for a thermodynamically relevant singular potential. |
| title | Navier-Stokes-Cahn-Hilliard equations on evolving surfaces |
| topic | Analysis of PDEs 35K59 (Primary) 35Q35, 35K67 (Secondary) |
| url | https://arxiv.org/abs/2401.12044 |