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On the partial regularity for solutions of the Navier-Stokes<br/><br/>system

Thursday, February 25, 2010 - 11:30am - 12:15pm
EE/CS 3-180
Igor Kukavica (University of Southern California)
Keywords: Navier-Stokes equations, partial regularity,
Hausdorff dimension, fractal dimension.

Abstract: A classical result of Caffarelli, Kohn, and Nirenberg states
that the one dimensional Hausdorff measure of singularities
of a suitable weak solution of the Navier-Stokes system is
zero. We present a short proof of the partial regularity
result which allows the force to belong to a singular Morrey
space. We also provide a new upper bound for the fractal
dimension of the singular set.
MSC Code: 
35Q30