# Dynamic bifurcation and instability of Dean problem

## TL;DR

This paper develops a nonlinear dynamic bifurcation theory for the Dean problem, providing rigorous justification for linear theories and analyzing vortex structures and instabilities.

## Contribution

It introduces a nonlinear theory for the Dean problem, rigorously justifies linear approximations, and applies dynamic bifurcation theory to analyze vortex structures and instabilities.

## Key findings

- Rigorous justification of linear theory for Dean problem
- Identification of vortex structures during bifurcation
- Analysis of instability mechanisms in fluid flow

## Abstract

The main objective of this paper is to address the instability and dynamical bifurcation of the Dean problem. A nonlinear theory is obtained for the Dean problem, leading in particular to rigorous justifications of the linear theory used by physicists, and the vortex structure. The main technical tools are the dynamic bifurcation theory [15] developed recently by Ma and Wang.