AN ASYMPTOTIC EXPANSION FOR PERTURBATIONS IN THE VELOCITY FIELD OF A STOKES SYSTEM DUE TO THE PRESENCE OF THIN INTERFACES

We consider the Stokes system for a viscous medium consisting of a thin inclusion having no uniform thickness merged in consistent background medium. Based on layer potential methods we rigorously derive an asymptotic expansion for two-dimensional velocity field associated with thin inclusion. We extend these techniques to determine a relationship between Stokes solutions measurements and the shape of the thin impurity.