Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain. (English) Zbl 1101.35356

Takahashi, Takéo

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.

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