### Abstract

We perform a mathematical analysis of the steady flow of a viscous liquid, L, past a three-dimensional elastic body, B. We assume that L fills the whole space exterior to B, and that its motion is governed by the Navier-Stokes equations corresponding to non-zero velocity at infinity, v_{∞}. As for B, we suppose that it is a St. Venant-Kirchhoff material, held in equilibrium either by keeping an interior portion of it attached to a rigid body or by means of appropriate control body force and surface traction. We treat the problem as a coupled steady state fluid-structure problem with the surface of B as a free boundary. Our main goal is to show existence and uniqueness for the coupled system liquid-body, for sufficiently small v_{∞} This goal is reached by a fixed point approach based upon a suitable reformulation of the Navier-Stokes equation in the reference configuration, along with appropriate a priori estimates of solutions to the corresponding Oseen linearization and to the elasticity equations.

Original language | English |
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Pages (from-to) | 849-875 |

Number of pages | 27 |

Journal | Archive for Rational Mechanics and Analysis |

Volume | 194 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Oct |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering

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## Cite this

*Archive for Rational Mechanics and Analysis*,

*194*(3), 849-875. https://doi.org/10.1007/s00205-009-0224-y