Maximum amplification of enstrophy in three-dimensional Navier–Stokes flows

This investigation concerns a systematic search for potentially singular behaviour in three-dimensional (3-D) Navier–Stokes flows. Enstrophy serves as a convenient indicator of the regularity of solutions to the Navier Stokes system – as long as this quantity remains finite, the solutions are guaranteed to be smooth and satisfy the equations in the classical (pointwise) sense. However, there are no estimates available with finite …