English

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

Analysis of PDEs 2009-07-14 v2

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 L˙1,1\dot L^{1,1}, and in the Sobolev spaces HsH^s for s>3/4s > 3/4. This builds on previous work in 1+1 dimensions of Pohlmeyer, Gu, Ginibre-Velo and Shatah.

Keywords

Cite

@article{arxiv.math/9807171,
  title  = {Local and global well-posedness of wave maps on $\R^{1+1}$ for rough data},
  author = {Marcus Keel and Terence Tao},
  journal= {arXiv preprint arXiv:math/9807171},
  year   = {2009}
}

Comments

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