Local well-posedness of the equations governing the motion of a fluid-filled elastic solid

Abstract

We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear elasticity, whereas the fluid motion is described by the Navier-Stokes equations. We prove that the governing equations admit a unique strong solution corresponding to non-zero initial data for the solid initial displacement and velocity, and for a fluid initial velocity in $H^{5/2}$.