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Nonsymmetric bifurcations of solutions of the 2D Navier-Stokes system. (English) Zbl 1237.35128

Nonsymmetric bifurcations for solutions to the Navier-Stokes system in two dimensions with periodic boundary conditions are studied in this paper. The dynamics of critical points of the stream function is studied. Three main results are proved. The first one provides a set of initial values such that critical points bifurcate from 1 to 2 and then to 3 in finite times; the second one describes merging from 3 to 2 and then to 1 solutions. The last one concerns existence of vortices without initial critical points.

MSC:

35Q30 Navier-Stokes equations
35B32 Bifurcations in context of PDEs
37G10 Bifurcations of singular points in dynamical systems
37G40 Dynamical aspects of symmetries, equivariant bifurcation theory
37G20 Hyperbolic singular points with homoclinic trajectories in dynamical systems
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