Abstract
The main objective of this paper is to study the stability and the type of transition of the Taylor problem in the wide-gap case by using the averaging method, and we conclude that the stability of the Taylor problem in the wide-gap case is essentially the same with that in the case of the narrow-gap. The main technical tools are the spectral theory for linear and completely continuous fields, the dynamic bifurcation theory and the transition theory for incompressible flows, both developed by Ma and Wang (Bifurcation Theory and Applications, 2005; Stability and Bifurcation of Nonlinear Evolution Equations, 2007).
Highlights
1 Introduction In, Taylor [ ] observed and studied the stability of laminar flow, which is known as the Couette flow
Ma and Wang established a new notion of bifurcation, called an attractor bifurcation, which was applied to the Taylor problem and obtained a series of fine results
This paper focuses on the Taylor problem in the wide-gap case
Summary
In , Taylor [ ] observed and studied the stability of laminar flow, which is known as the Couette flow. This paper focuses on the Taylor problem in the wide-gap case. The main technical tools are the spectral theory for linear and completely continuous fields, the dynamic bifurcation theory and the transition theory for incompressible flows These theories are directly applied to the Taylor problem in the wide-gap case. The main theorems are presented in Section , through which we can give pictures depicting the Couette flow stability in the wide-gap case, and compare with the Taylor problem in the narrow-gap case. Section studies the Taylor problem in the wide-gap case by using the averaging method, and establishes its mathematical frame. Explains that in the wide-gap case, the Couette flow of the Taylor problem is metastable. Give the entire results of stability of the Taylor problem in the wide-gap case; see Figure .
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