Asymptotical Behavior of Global Solutions of the Navier-Stokes-Korteweg Equations with Respect to Capillarity Number at Infinity
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916591910780928 |
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| author | Jiang, Fei Li, Pengfei Wang, Jiawei |
| author_facet | Jiang, Fei Li, Pengfei Wang, Jiawei |
| contents | Vanishing capillarity in the Navier-Stokes-Korteweg (NSK) equations has been widely investigated, in particular, it is well-known that the NSK equations converge to the Navier-Stokes (NS) equations by vanishing capillarity number. To our best knowledge, this paper first investigates the behavior of large capillary number, denoted by $κ^2$, for the global(-in-time) strong solutions with small initial perturbations of the three-dimensional (3D) NSK equations in a slab domain with Navier(-slip) boundary condition. Under the well-prepared initial data, we can construct a family of global strong solutions of the 3D incompressible NSK equations with respect to $κ>0$, where the solutions converge to a unique solution of 2D incompressible NS-like equations as $κ$ goes to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotical Behavior of Global Solutions of the Navier-Stokes-Korteweg Equations with Respect to Capillarity Number at Infinity Jiang, Fei Li, Pengfei Wang, Jiawei Analysis of PDEs Vanishing capillarity in the Navier-Stokes-Korteweg (NSK) equations has been widely investigated, in particular, it is well-known that the NSK equations converge to the Navier-Stokes (NS) equations by vanishing capillarity number. To our best knowledge, this paper first investigates the behavior of large capillary number, denoted by $κ^2$, for the global(-in-time) strong solutions with small initial perturbations of the three-dimensional (3D) NSK equations in a slab domain with Navier(-slip) boundary condition. Under the well-prepared initial data, we can construct a family of global strong solutions of the 3D incompressible NSK equations with respect to $κ>0$, where the solutions converge to a unique solution of 2D incompressible NS-like equations as $κ$ goes to infinity. |
| title | Asymptotical Behavior of Global Solutions of the Navier-Stokes-Korteweg Equations with Respect to Capillarity Number at Infinity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.18902 |