Criticality of the Navier-Stokes equations with respect to hyper-dissipation

Criticality of the Navier-Stokes equations with respect to hyper-dissipation

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Liaosha Xu, University of Virginia

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.