Bifurcations of Solutions of the 2-Dimensional Navier–Stokes System

  • Dong Li
  • Yakov G. Sinai


For the 2-dimensional Navier–Stokes System written for the stream functions we construct a set of initial data for which initial critical points bifurcate into three critical points. This can be interpreted as the birth of new viscous vortices from a single one. In another class of solutions vortices merge, i.e. the number of critical points decrease.


Initial Data Periodic Orbit Extremal Point Stream Function Degenerate Case 
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The authors thank V. Yakhot for useful remarks and discussions. The first author is supported in part by a start-up fund from University of British Columbia. The financial support from NSF, grant DMS 0908032, given to the first author and grant DMS060096, given to the second author are highly appreciated.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Deparment of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  3. 3.Landau Institute of Theoretical PhysicsMoscowRussia

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