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.
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Notes
- 1.
Strictly speaking, we should consider the Galerkin approximations of our system to avoid issues connected with the infinite dimensionality of our system.
References
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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.
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Dedicated to the 80th Anniversary of Professor Stephen Smale
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Li, D., Sinai, Y.G. (2012). Bifurcations of Solutions of the 2-Dimensional Navier–Stokes System. In: Pardalos, P., Rassias, T. (eds) Essays in Mathematics and its Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28821-0_10
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DOI: https://doi.org/10.1007/978-3-642-28821-0_10
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