On the weak solution of the fluid-structure interaction problem for shear-dependent Fluids

Abstract

In this paper the coupled fluid-structure interaction problem for incompressible non-Newtonian shear-dependent fluid flow in two-dimensional time dependent domain is studied. One part of the domain boundary consists of an elastic wall. Its temporal evolution is governed by the generalized string equation with action of the fluid forces by means of the Neumann type boundary condition. The aim of this work is to present the limiting process for the auxiliary (κ, ϵ, k)-problem. The weak solution of this auxiliary problem has been studied in our recent work (Hundertmark-Zaušková, Lukáčová-Medvidová, Necasová, On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid, J. Math. Soc. Japan (in press)).