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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2506.16105 |
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| _version_ | 1866912440137023488 |
|---|---|
| author | Lv, Maoyin |
| author_facet | Lv, Maoyin |
| contents | We investigate the Abels-Garcke-Grün model that describes the motion of two viscous incompressible fluids with unmatched densities in the presence of a uniform gravitational field. For the perturbated system with respect to a given equilibrium state in three dimensions, we establish the local existence and uniqueness of a strong solution using a suitable iteration scheme and the energy method. This work lays the foundation for further studies on the Rayleigh-Taylor instability problem of nonhomogeneous two-phase flows within the framework of diffuse interface models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16105 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local well-posedness of a perturbation problem for the Abels-Garcke-Grün model in three dimensions Lv, Maoyin Analysis of PDEs We investigate the Abels-Garcke-Grün model that describes the motion of two viscous incompressible fluids with unmatched densities in the presence of a uniform gravitational field. For the perturbated system with respect to a given equilibrium state in three dimensions, we establish the local existence and uniqueness of a strong solution using a suitable iteration scheme and the energy method. This work lays the foundation for further studies on the Rayleigh-Taylor instability problem of nonhomogeneous two-phase flows within the framework of diffuse interface models. |
| title | Local well-posedness of a perturbation problem for the Abels-Garcke-Grün model in three dimensions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.16105 |