Electron. J. Diff. Eqns., Vol. 1999(1999), No. 48, pp. 1-8.

On the smallness of the (possible) singular set in space for 3D Navier-Stokes equations

Zoran Grujic

Abstract:
We utilize $L^\infty$ estimates on the complexified solutions of 3D Navier-Stokes equations via a plurisubharmonic measure type maximum principle to give a short proof of the fact that the Hausdorff dimension of the (possible) singular set in space is less or equal 1 assuming chaotic, Cantor set-like structure of the blow-up profile.

Submitted August 20, 1999. Published December 3, 1999.
Math Subject Classifications: 35Q30, 76D03.
Key Words: Navier-Stokes equations, singular set, turbulence.

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Zoran Grujic
Department of Mathematics
University of Texas
Austin, TX 78712, USA
e-mail: grujic@math.utexas.edu
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