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

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

1998-07-30

arxiv.org/abs/math/9807171v2

IMRN 21 (1998), 1117-1156

Mathematics

Analysis of PDEs

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

Scientific paper

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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