Viscous fluid-thin cylindrical elastic body interaction: asymptotic analysis on contrasting properties

Abstract

ABSTRACTA periodic, axially symmetric time-dependent model of interaction between a viscous fluid and a thin cylindrical elastic tube is considered. The problem depends on a small parameter , representing the ratio of the thickness of the wall and the radius of the cylinder. We consider Young’s modulus of the elastic medium and its density great or small parameters equal to some powers of . An asymptotic expansion is constructed for various magnitudes of the rigidity and of the density of the elastic tube. The generality of the considered model requires to take into account six different combinations of the three parameters depending on . We obtain in this way different limit problems which are Stokes equations with some special boundary conditions. The expansion is justified by the high-order estimates for the difference of the exact solution and truncated asymptotic approximation.