Existence and uniqueness result for Stokes flows in a half-plane

Abstract

This paper is concerned with the study of the two-dimensional Stokes flow past a smooth obstacle near a plane wall. Using the boundary integral formulation, the flow is represented in terms of a combined distribution of a single-layer and a double-layer potentials of Green's functions over the boundary of the obstacle. The problem is formulated as a set of Fredholm integral equations of the second kind for the density of the potentials. The existence and uniqueness results of the solution are obtained. Numerical results are presented in the case of a rigid circular obstacle moving parallel or normal to the plane wall.