The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911899222802432 |
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| author | He, Jiao Su, Pei |
| author_facet | He, Jiao Su, Pei |
| contents | We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of the fluid-structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_16257 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid He, Jiao Su, Pei Analysis of PDEs 35B40, 76D05, 35Q70, 35Q35, 35Q30 We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $\rline^3$. When the small rigid body shrinks to a "massless" point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates of the fluid-structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit. |
| title | The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid |
| topic | Analysis of PDEs 35B40, 76D05, 35Q70, 35Q35, 35Q30 |
| url | https://arxiv.org/abs/2211.16257 |