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 time dependent local structure, then time independent bounds 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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Communicated by G.P. Galdi
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Bradshaw, Z., Grujić, Z. Blow-Up Scenarios for the 3D Navier–Stokes Equations Exhibiting Sub-Criticality with Respect to the Scaling of One-Dimensional Local Sparseness. J. Math. Fluid Mech. 16, 321–334 (2014). https://doi.org/10.1007/s00021-013-0155-0
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DOI: https://doi.org/10.1007/s00021-013-0155-0