Remarks of global wellposedness of liquid crystal flows and heat flows of harmonic maps in two dimensions

Zhen Lei, Dong Li, Xiaoyi Zhang

Type: Article

Publication Date: 2014-07-29

Citations: 66

DOI: https://doi.org/10.1090/s0002-9939-2014-12057-0

Abstract

We consider the Cauchy problem to the two-dimensional incompressible liquid crystal equation and the heat flows of the harmonic maps equation. Under a natural geometric angle condition, we give a new proof of the global wellposedness of smooth solutions for a class of large initial data in energy space. This result was originally obtained by Ding-Lin and Lin-Lin-Wang. Our main technical tool is a rigidity theorem which gives the coercivity of the harmonic energy under a certain angle condition. Our proof is based on a frequency localization argument combined with the concentration-compactness approach which can be of independent interest.

Locations

Proceedings of the American Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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