Some applications of parabolic Dirac operators to the instationary Navier-Stokes problem on conformally flat cylinders and tori in $\mathbb{R}^3$

Abstract

In this paper we give a survey on how to apply recent techniques of Clifford analysis over conformally flat manifolds to deal with instationary flow problems on cylinders and tori. Solutions are represented in terms of integral operators involving explicit expressions for the Cauchy kernel that are associated to the parabolic Dirac operators acting on spinor sections of these manifolds.