Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses Positions Contact 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.aviRecording (mp4): http://mm.math.cmu.edu/recordings/cna/CNA-HuangTao-Oct-11-2012.mp4Date: Thursday, October 11, 2012Time: 1:30 pmLocation: Wean 7218Submitted by:  David Kinderlehrer