On the Dirichlet Problem for the Stokes System in Multiply Connected Domains

Abstract

The Dirichlet problem for the Stokes system in a multiply connected domain of ${ℝ}^n(n\ge 2)$ is considered in the present paper. We give the necessary and sufficient conditions for the representability of the solution by means of a simple layer hydrodynamic potential, instead of the classical double layer hydrodynamic potential.