Zoom link: https://princeton.zoom.us/j/9148065146

Some further results have been developed for showing the critical nature of the Navier-Stokes equations.  In particular, it is proved that the global-in-time regular solutions exist for the Navier-Stokes equations with hyper-dissipation, with the hypotheses that there is one singular point in space, the flow exhibits certain symmetries and is "periodically focusing" near the singular point.