Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866909108162002944 |
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| author | Schwarzacher, Sebastian Su, Pei |
| author_facet | Schwarzacher, Sebastian Su, Pei |
| contents | A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The coupling is partially of geometric nature, as the geometry of the fluid domain is changing in accordance to the motion of the beam. Here the existence of a unique strong solution for large initial data and all times up to geometric degeneracy is shown. For that an a-priori estimate on the time-derivative of the coupled solution is introduced. For the Navier-Stokes part it is a borderline estimate in the spirit of Ladyzhenskaya applied directly to the in-time differentiated system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04253 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations Schwarzacher, Sebastian Su, Pei Analysis of PDEs 35B65, 35Q74, 74F10, 35R37, 76D03 A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The coupling is partially of geometric nature, as the geometry of the fluid domain is changing in accordance to the motion of the beam. Here the existence of a unique strong solution for large initial data and all times up to geometric degeneracy is shown. For that an a-priori estimate on the time-derivative of the coupled solution is introduced. For the Navier-Stokes part it is a borderline estimate in the spirit of Ladyzhenskaya applied directly to the in-time differentiated system. |
| title | Existence of strong solutions for a perfect elastic beam interacting with Navier-Stokes equations |
| topic | Analysis of PDEs 35B65, 35Q74, 74F10, 35R37, 76D03 |
| url | https://arxiv.org/abs/2308.04253 |