Compressible fluids and elastic plates in 2D: A conditional no-contact theorem
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913571167797248 |
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| author | Breit, Dominic Roy, Arnab |
| author_facet | Breit, Dominic Roy, Arnab |
| contents | We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The displacement of the latter evolves according to a beam equation. Both are coupled through kinematic boundary conditions and the balance of forces. We prove that for any weak solution to the coupled system, which satisfies certain additional regularity requirements, no contact occurs between the elastic wall and the bottom of the fluid cavity. This applies to both isentropic and heat-conducting fluids. As a special case of our general theory we extend the unconditional result from Grandmont and Hillairet (Arch. Ration. Mech. Anal. 220, 1283--1333, 2016) on incompressible fluids from visco-elastic to perfectly elastic plates. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_01994 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compressible fluids and elastic plates in 2D: A conditional no-contact theorem Breit, Dominic Roy, Arnab Analysis of PDEs 35B65, 35Q74, 35R37, 74F10, 74K25 We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The displacement of the latter evolves according to a beam equation. Both are coupled through kinematic boundary conditions and the balance of forces. We prove that for any weak solution to the coupled system, which satisfies certain additional regularity requirements, no contact occurs between the elastic wall and the bottom of the fluid cavity. This applies to both isentropic and heat-conducting fluids. As a special case of our general theory we extend the unconditional result from Grandmont and Hillairet (Arch. Ration. Mech. Anal. 220, 1283--1333, 2016) on incompressible fluids from visco-elastic to perfectly elastic plates. |
| title | Compressible fluids and elastic plates in 2D: A conditional no-contact theorem |
| topic | Analysis of PDEs 35B65, 35Q74, 35R37, 74F10, 74K25 |
| url | https://arxiv.org/abs/2411.01994 |