### Abstract

We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B, L}, which means that there exists a frame with respect to which the relevant governing equations possess a timeindependent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.

Original language | English |
---|---|

Pages (from-to) | 1-102 |

Number of pages | 102 |

Journal | Memoirs of the American Mathematical Society |

Volume | 226 |

Issue number | 1060 |

DOIs | |

Publication status | Published - 2013 Nov |

Externally published | Yes |

### Keywords

- Fluid-structure interaction
- Navier-Stokes
- Nonlinear elasticity

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

## Fingerprint Dive into the research topics of 'On the steady motion of a coupled system solid-liquid'. Together they form a unique fingerprint.

## Cite this

Bemelmans, J., Galdi, G. P., & Kyed, M. (2013). On the steady motion of a coupled system solid-liquid.

*Memoirs of the American Mathematical Society*,*226*(1060), 1-102. https://doi.org/10.1090/S0065-9266-2013-00678-8