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arXiv · 1502.06265

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

Radu Dascaliuc·Zoran Grujić·Michael S. Jolly
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Abstract

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 (exponential in Grashof), in marked contrast to the subcritical case, $r>1/2$ (algebraic in Grashof).

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Radu Dascaliuc, Zoran Grujić, Michael S. Jolly. 2015-02-22. Effect of vorticity coherence on energy-enstrophy bounds for the 3D Navier-Stokes equations. https://doi.org/10.1007/s00021-015-0216-7

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