Abstract

Extinction and blowup of weak solutions to the Navier-Stokes equations

Koji Ohkitani
University of Sheffield

We study blowup problems of the Navier-Stokes weak solutions with attention to
the evolution critical norms, which is expected to be transcendental in time.
If the product of energy and enstrophy has a "logarithmic" upper-bound in time,
then energy converges to zero (extinction) upon blowup. By a simple analysis based
on the known enstrophy bounds, we derive a constraint on the rate of the extinction.
We also explore a possibility of considering Leray's dynamically-scaled equations
in weak form.