Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
CNA Seminar/Colloquium
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: http://mm.math.cmu.edu/recordings/cna/CNA-HuangTao-Oct-11-2012.aviRecording: 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 |