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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.