On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916056702910464 |
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| author | Bravin, Marco Feireisl, Eduard Roy, Arnab Zarnescu, Arghir |
| author_facet | Bravin, Marco Feireisl, Eduard Roy, Arnab Zarnescu, Arghir |
| contents | We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the problem based on a combination of the approach proposed by Judakov with a suitable form of energy inequality. We show that global--in--time dissipative solutions always exist as long as the rigid bodies are connected compact sets. In addition, in the absence of external driving forces, the system always tends to a static equilibrium as time goes to infinity. The results hold independently of possible collisions of rigid bodies and for any finite energy initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid Bravin, Marco Feireisl, Eduard Roy, Arnab Zarnescu, Arghir Analysis of PDEs 35Q35, 35B40, 74F10, 76D03 We consider several rigid bodies immersed in a viscous Newtonian fluid contained in a bounded domain in $R^3$. We introduce a new concept of dissipative weak solution of the problem based on a combination of the approach proposed by Judakov with a suitable form of energy inequality. We show that global--in--time dissipative solutions always exist as long as the rigid bodies are connected compact sets. In addition, in the absence of external driving forces, the system always tends to a static equilibrium as time goes to infinity. The results hold independently of possible collisions of rigid bodies and for any finite energy initial data. |
| title | On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid |
| topic | Analysis of PDEs 35Q35, 35B40, 74F10, 76D03 |
| url | https://arxiv.org/abs/2505.04372 |