| Abstract: |
| It remains an open problem whether or not solutions to the 3D Navier-Stokes equations with smooth data remain smooth for all time.
All previously known regularity criteria are formulated in times of a blow-up time (where the solution loses smoothness), which make it practically impossible to use such necessary conditions to test the viability of certain numerically computed candidates.
Motivated by these issues, we give the first quantitative classification of potentially singular solutions at any given time in the region of potential blow-up times. The quantitative lower bounds prior to any potential blow-up time (and in the open vicinity of it) are in principle amenable to numerical testing. |
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