Well-posedness theorems in fluid-structure interaction: perfectly elastic shells
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918501118115840 |
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| author | Breit, Dominic Mensah, Prince Romeo Schwarzacher, Sebastian Su, Pei |
| author_facet | Breit, Dominic Mensah, Prince Romeo Schwarzacher, Sebastian Su, Pei |
| contents | In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the Navier--Stokes equations. Consequently, damping within the coupled system comes entirely from the parabolic fluid subsystem. Our main result is the construction of a local-in-time unique strong solution to the system of PDEs. Standard techniques from the literature do not apply here. They are restricted to visco-elastic structures, where the corresponding solid phase is parabolic. Our construction relies on a different method built upon a new estimate for the acceleration of the system. In the case of a 2D viscous incompressible fluid interacting with a 1D perfectly elastic shell we can extend the local solution globally in time (until a possible self-intersection of the shell). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14357 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness theorems in fluid-structure interaction: perfectly elastic shells Breit, Dominic Mensah, Prince Romeo Schwarzacher, Sebastian Su, Pei Analysis of PDEs In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the Navier--Stokes equations. Consequently, damping within the coupled system comes entirely from the parabolic fluid subsystem. Our main result is the construction of a local-in-time unique strong solution to the system of PDEs. Standard techniques from the literature do not apply here. They are restricted to visco-elastic structures, where the corresponding solid phase is parabolic. Our construction relies on a different method built upon a new estimate for the acceleration of the system. In the case of a 2D viscous incompressible fluid interacting with a 1D perfectly elastic shell we can extend the local solution globally in time (until a possible self-intersection of the shell). |
| title | Well-posedness theorems in fluid-structure interaction: perfectly elastic shells |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.14357 |