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arXiv · 1303.0257

Blow-up scenarios for 3D NSE exhibiting sub-criticality with respect to the scaling of one-dimensional local sparseness

Zachary Bradshaw·Zoran Grujic
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Abstract

It is shown that, if the vorticity magnitude associated with a (presumed singular) three-dimensional incompressible Navier-Stokes flow blows-up in a manner exhibiting certain {\em time dependent local structure}, then {\em time independent} estimates on the $L^1$ norm of $|\omega|\log\sqrt{1+ |\omega|^2}$ follow. The implication is that the volume of the region of high vorticity decays at a rate of greater order than a rate connected to the critical scaling of one-dimensional local sparseness and, consequently, the solution becomes sub-critical.

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Zachary Bradshaw, Zoran Grujic. 2013-03-01. Blow-up scenarios for 3D NSE exhibiting sub-criticality with respect to the scaling of one-dimensional local sparseness. https://doi.org/10.1007/s00021-013-0155-0

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