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

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.

1 picture, 34 pages. As pointed out to us by Kenji Nakanishi, the proof of local well-posedness was only valid for s>3/4, and the paper has been amended accordingly

References in corpus (1)

• Ill-posedness for one-dimensional wave maps at the critical regularity

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