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Stability and Bifurcation of the Taylor Problem

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Abstract

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].

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, P. R. China

    Tian Ma

  2. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Shouhong Wang

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  1. Tian Ma
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  2. Shouhong Wang
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Correspondence to Shouhong Wang.

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Communicated by T-P Liu

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Ma, T., Wang, S. Stability and Bifurcation of the Taylor Problem. Arch. Rational Mech. Anal. 181, 149–176 (2006). https://doi.org/10.1007/s00205-006-0415-8

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  • DOI: https://doi.org/10.1007/s00205-006-0415-8

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