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Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data

Marcus Keel·Terence Tao
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Abstract

We prove local and global existence from large, rough initial data for a wave map between 1+1 dimensional Minkowski space and an analytic manifold. Included here is global existence for large data in the scale-invariant norm $\dot L^{1,1}$, and in the Sobolev spaces $H^s$ for $s > 3/4$. This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.

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Marcus Keel, Terence Tao. 2009-07-14. Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data. https://arxiv.org/abs/math/9807171

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