## Abstract

We consider the 2D Navier-Stokes system written for the stream function with periodic boundary conditions and construct a set of initial data such that initial critical points bifurcate from 1 to 2 and then to 3 critical points in finite time. The bifurcation takes place in a small neighborhood of the origin. Our construction does not require any symmetry assumptions or the existence of special fixed points. For another set of initial data we show that 3 critical points merge into 1 critical point in finite time. We also construct a set of initial data so that bifurcation can be generated by the Navier-Stokes flow and do not require the existence of an initial critical point.

Original language | English (US) |
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Pages (from-to) | 1976-1999 |

Number of pages | 24 |

Journal | Advances in Mathematics |

Volume | 229 |

Issue number | 3 |

DOIs | |

State | Published - Feb 15 2012 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Bifurcations
- Navier-Stokes equations