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

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.