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CNA Seminar
Tao Huang
University of Kentucky
Title: Some new results on the uniqueness of heat flow of harmonic maps and nematic liquid crystal flows

Abstract: We establish the uniqueness of heat flow of harmonic maps into a unit sphere S that have sufficiently small renormalized energies. For such a class of weak solutions, we also establish the convexity property of the Dirichlet energy for $t > t_0 > 0$ and the unique limit property at time infinity. As a corollary, we obtain the uniqueness for heat flow of harmonic maps whose gradients belong to $L^p_tL^q_x$ for $p > 2$, $q > n$ and $(p,q)$ satisfying the Serrin condition. We also establish the uniqueness for hydrodynamic flow $(u,d)$ of nematic liquid crystals, with $(u,\nabla d)$ satisfying the Serrin condition. This is joint work with Prof. Changyou Wang.

Recording (avi): http://mm.math.cmu.edu/recordings/cna/CNA-HuangTao-Oct-11-2012.avi
Recording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-HuangTao-Oct-11-2012.mp4
Date: Thursday, October 11, 2012
Time: 1:30 pm
Location: Wean 7218
Submitted by:  David Kinderlehrer