Small pertubations of an interface for Stokes system

Abstract

We consider the Stokes system for a viscous medium consisting of an impurely (inclusion) merged in a consistent background medium. Appointed on both field expansion and layer potential methods, we strictly derive the asymptotic expansion of the perturbed velocity field because of small perturbations in the interface of the inclusion. We use these techniques to determine a relationship between Stokes solutions measurements and the shape of the object. Moreover, we may prove an asymptotic expansion for the perturbation in the viscosity moment tensors (VMTs) caused by the presence of small changes in the interface of the impurity. K E Y W O R D Sasymptotic expansions, boundary integral method, interface problem, small perturbations, Stokes system, viscous moment tensors