## Effect of vorticity coherence on energy-enstrophy bounds for the 3D Navier-Stokes equations

#### Michael JollyIndiana University

Bounding curves in the energy,enstrophy-plane are derived for the 3D Navier-Stokes equations
under an assumption on coherence of the vorticity direction. The analysis in the critical case where the
direction is H\"older continuous with exponent $r=1/2$ results in a curve with extraordinarily large maximal enstrophy, in marked contrast to the subcritical case, $r>1/2$. Joint work with R. Dascaluic and Z. Grujic.

Back to Workshop I: Mathematical Analysis of Turbulence