Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915011074457600 |
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| author | Ding, Shijin Li, Yinghua Lin, Zhilin Yan, Yuanxiang |
| author_facet | Ding, Shijin Li, Yinghua Lin, Zhilin Yan, Yuanxiang |
| contents | In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is the phase field model for the moving contact line problem in fluid mechanics. We establish the existence and uniqueness of local-in-time strong solution to this initial boundary value problem in 2D. To our knowledge, this is the first result to give the local-in-time well-posedness of Navier-Stokes/Cahn-Hilliard system with generalized Navier boundary condition and relaxation boundary condition. This result provides a rigorous mathematical analysis to confirm that the physical and numerical results by Qian-Wang-Sheng [Phys. Rev. E 68 (2003), 016306, 1-15; J. Fluid Mech. 564 (2006), 333-360] are well-posed and reasonable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel Ding, Shijin Li, Yinghua Lin, Zhilin Yan, Yuanxiang Analysis of PDEs In this paper, we study the contact line problem in a channel. Precisely, we consider the incompressible Navier-Stokes/Cahn-Hilliard system with eneralized Navier boundary condition and relaxation boundary condition in a channel, which is the phase field model for the moving contact line problem in fluid mechanics. We establish the existence and uniqueness of local-in-time strong solution to this initial boundary value problem in 2D. To our knowledge, this is the first result to give the local-in-time well-posedness of Navier-Stokes/Cahn-Hilliard system with generalized Navier boundary condition and relaxation boundary condition. This result provides a rigorous mathematical analysis to confirm that the physical and numerical results by Qian-Wang-Sheng [Phys. Rev. E 68 (2003), 016306, 1-15; J. Fluid Mech. 564 (2006), 333-360] are well-posed and reasonable. |
| title | Well-posedness of Navier-Stokes/Cahn-Hilliard equations modeling the dynamics of contact line in a channel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2312.17520 |