AMMCS-2011 Plenary Talk:

Lower Bounds on the Navier-Stokes Singular Set

by Walter Craig

McMaster University

The well-known result of partial regularity for solutions of the Navier-Stokes equations provides an upper bound on the size of the singular set of (suitable) weak solutions. This talk will describe complementary lower bounds, both for the the singular set and the energy (L²) concentration set, in case that they are nonempty. These bounds are microlocal in nature, and are based on a novel estimate for weak solutions of the Navier-Stokes equations.

Part of these results represents joint work with A. Biryuk and M. Arnold.

Walter Craig is currently a professor of mathematics and a Canada Research Chair at McMaster University. He was an undergraduate at Berkeley, and and he received his PhD from the Courant Institute. Prior to his move to McMaster he was on the faculty of Caltech, Stanford University and Brown University. He is a Fellow of the Royal Society of Canada, and he presently holds a Killam Research Fellowship.