Abstract
In this paper, we study the real analytic regularity and bifurcations of the solutions for the two-dimensional periodic Boussinesq system. If the critical points of the stream function ψ are points of maxima or minima, one shall call these points viscous vortices because near these points the velocity u is tangent to the level sets of ψ which is a closed curve. For any smooth initial temperature θ0, we can construct a set of initial stream functions 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. For another set of initial stream functions, we show that 3 critical points merge into 1 critical point in finite time. We also construct a set of initial stream functions so that bifurcation can be generated without the existence of an initial critical point.
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