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Schrödinger Maps and their associated Frame Systems

Andrea Nahmod·Jalal Shatah·Luis Vega·Chongchun Zeng
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Abstract

In this paper we establish the equivalence of solutions between Schrödinger map into $\mathbb{S}^2$ or $ \mathbb{H}^2$ and their associated gauge invariant Schrödinger equations. We also establish the existence of global weak solutions into $\mathbb{H}^2$ in two space dimensions. We extend these ideas for maps into compact hermitian symmetric manifolds with trivial first cohomology.

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Andrea Nahmod, Jalal Shatah, Luis Vega, Chongchun Zeng. 2007-01-30. Schrödinger Maps and their associated Frame Systems. https://arxiv.org/abs/math/0612481

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