Elliptic boundary value problems of fluid dynamics over unbounded domains

In this paper We develop a Clifford operator calculus over unbounded domain s whose complement contains a non-empty open set by using add-on terms to t he Cauchy kernel. Using the knowledge about the Poisson equation allows us to prove a direct decomposition of the space L-q(Omega), which will be appl ied to solve the linear Stokes problem in scales of W-q(k)(Omega)-spaces ov er this kind of unbounded domains. This result will be used to investigate the Navier-Stokes equations by means of a Banach contraction:principle. In the end, steady solutions of stream problems with free convection will. be studied. Copyright (C) 2000 John Wiley & Sons, Ltd.