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arXiv · 1205.1269

Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions

Zhen Lei·Dong Li·Xiaoyi Zhang
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Abstract

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

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Zhen Lei, Dong Li, Xiaoyi Zhang. 2012-10-05. Remarks of Global Wellposedness of Liquid Crystal Flows and Heat Flows of Harmonic Maps in Two Dimensions. https://arxiv.org/abs/1205.1269

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