PIMS/UVic Lecture: Walter Craig

Walter holds a CRC for Mathematical Analysis and its Applications at McMaster University, and was recently elected a fellow of the Royal Society of Canada. Before moving to Canada he has been on the faculty of Caltech, Stanford University, and was chair of the Mathematics  Department at Brown University.

Abstract:

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 (L^2 norm) concentration set, in case that they are nonempty. These bounds are microlocal in nature, and follow from a novel estimate for weak solutions of the Navier-Stokes equations. These results are, in part, joint work with M. Arnold, and the above estimate on weak solutions was originally described by A. Biryuk, S. Ibrahim and myself.