Takahashi, Takéo Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. (English) Zbl 1101.35356 Adv. Differ. Equ. 8, No. 12, 1499-1532 (2003). Summary: We study a fluid-rigid-body interaction problem. The motion of the fluid is modeled by the Navier-Stokes equations, written in an unknown bounded domain depending on the displacement of the rigid body. Our main result yields existence and uniqueness of strong solutions. In the two-dimensional case, the solutions are global provided that the rigid body does not touch the boundary. In the three-dimensional case, we obtain local-in-time existence and global existence for small data. Moreover, we prove an asymptotic stability result. Cited in 1 ReviewCited in 56 Documents MSC: 35Q30 Navier-Stokes equations 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:fluid-rigid-body interaction; Navier-Stokes equations; existence; uniqueness; strong solutions; asymptotic stability PDF BibTeX XML Cite \textit{T. Takahashi}, Adv. Differ. Equ. 8, No. 12, 1499--1532 (2003; Zbl 1101.35356)