Existence of global weak solutions for the high frequency and small
displacement oscillation fluid-structure interactions systems
Abstract
The purpose of this paper is to study the fluid-structure interaction
(FSI) problem which is a simplified model to describe high frequency and
small displacement oscillation of elastic structure in fluids. The
elastic structure displacement is modeled by a fourth order nonlinear
hyperbolic square equations, the motion of fluid is modeled by the
time-dependent incompressible Navier-Stokes equations. we prove the
existence of at least one weak solutions (global in time) to this
problem by compactness method. The result both holds for two-dimensional
and three-dimensional cases.