Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions

@article{Tao2001GlobalRO,
  title={Global Regularity of Wave Maps¶II. Small Energy in Two Dimensions},
  author={Terence Tao},
  journal={Communications in Mathematical Physics},
  year={2001},
  volume={224},
  pages={443-544}
}
  • T. Tao
  • Published 22 November 2000
  • Mathematics
  • Communications in Mathematical Physics
Abstract: We show that wave maps from Minkowski space ℝ1+n to a sphere Sm−1 are globally smooth if the initial data is smooth and has small norm in the critical Sobolev space , in all dimensions n≥ 5. This generalizes the results in the prequel [40] of this paper, which addressed the high-dimensional case n≥ 5. In particular, in two dimensions we have global regularity whenever the energy is small, and global regularity for large data is thus reduced to demonstrating non-concentration of energy… 
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