On weak solutions of a control-volume model for liquid films flowing down a fibre
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909100969820160 |
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| author | Taranets, Roman M. Ji, Hangjie Chugunova, Marina |
| author_facet | Taranets, Roman M. Ji, Hangjie Chugunova, Marina |
| contents | This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial differential equations, which describe the fluid film's radius and axial velocity. We demonstrate the existence of weak solutions to this coupled system by applying a priori estimates derived from energy-entropy functionals. Additionally, we establish the existence of traveling wave solutions for the system. To illustrate our analytical findings, we present numerical studies that showcase the dynamic solutions of the partial differential equations as well as the traveling wave solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02720 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On weak solutions of a control-volume model for liquid films flowing down a fibre Taranets, Roman M. Ji, Hangjie Chugunova, Marina Analysis of PDEs Fluid Dynamics This paper presents an analytical investigation of the solutions to a control volume model for liquid films flowing down a vertical fibre. The evolution of the free surface is governed by a coupled system of degenerate nonlinear partial differential equations, which describe the fluid film's radius and axial velocity. We demonstrate the existence of weak solutions to this coupled system by applying a priori estimates derived from energy-entropy functionals. Additionally, we establish the existence of traveling wave solutions for the system. To illustrate our analytical findings, we present numerical studies that showcase the dynamic solutions of the partial differential equations as well as the traveling wave solutions. |
| title | On weak solutions of a control-volume model for liquid films flowing down a fibre |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2301.02720 |