Elliptic boundary value problems of fluid dynamics over unbounded domains

Abstract

In this paper we develop a Clifford operator calculus over unbounded domains whose complement contains a non-empty open set by using add-on terms to the Cauchy kernel. Using the knowledge about the Poisson equation allows us to prove a direct decomposition of the space , which will be applied to solve the linear Stokes problem in scales of -spaces over 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 © 2000 John Wiley & Sons, Ltd.