Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system

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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 languageEnglish (US)
Pages (from-to)1976-1999
Number of pages24
JournalAdvances in Mathematics
Volume229
Issue number3
DOIs
StatePublished - Feb 15 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Bifurcations
  • Navier-Stokes equations

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