PIMS/AMI Seminar: Dong Li

Abstract

I will explain some recent results (joint work with Ya.G. Sinai) on the bifurcation of solutions to the Navier-Stokes system.  We consider the stream function  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.