An approximation of the nonlinear fluid--structure interaction problem for a rotationally symmetric flow

Abstract

An approximation of the fluid-structure interaction problem in the cylindrical coordinate system is studied. First, we solve the free boundary problem by means of Schauder's fixed point theorem. After that, we regularize the linear viscoelastic cylindrical Koiter shell equation that was considered in [12], by adding  higher order terms in order to get the strong convergence of the second derivatives of a sequence of radial displacements. We need the strong convergence of the second derivatives in order to guarantee the strong convergence of corresponding divergence free test functions due to [8].