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

  • Dong Li
  • Yakov G. Sinai
Chapter

Abstract

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.

Keywords

Initial Data Periodic Orbit Extremal Point Stream Function Degenerate Case 
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Notes

Acknowledgements

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.

References

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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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