Stability and Bifurcation of the Taylor Problem

The main objective of this paper is to address the stability and bifurcation of the Couette flow between two concentric rotating cylinders, and to verify rigorously Taylor's observation in his experiments 13]. A nonlinear theory is obtained for the Taylor problem, leading in particular to rigorous justifications of the linear theory used by physicists, and the Taylor vortex structure. The main technical tools are the dynamic bifurcation theory and the geometric theory for incompressible flows, both developed recently by Ma & Wang 10, 12].