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arXiv · 1705.00260

Equivariant Schr\"odinger maps from two dimensional hyperbolic space

Jiaxi Huang·Youde Wang·Lifeng Zhao
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Abstract

In this article, we consider the equivariant Schr\"odinger map from $\Bbb H^2$ to $\Bbb S^2$ which converges to the north pole of $\Bbb S^2$ at the origin and spatial infinity of the hyperbolic space. If the energy of the data is less than $4\pi$, we show that the local existence of Schr\"odinger map. Furthermore, if the energy of the data sufficiently small, we prove the solutions are global in time.

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Jiaxi Huang, Youde Wang, Lifeng Zhao. 2017-04-30. Equivariant Schr\"odinger maps from two dimensional hyperbolic space. https://arxiv.org/abs/1705.00260

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