Ill-posedness for One-dimensional Wave Maps at the Critical Regularity

@inproceedings{TaoIllposednessFO,
  title={Ill-posedness for One-dimensional Wave Maps at the Critical Regularity},
  author={Terence Tao}
}
We show that the wave map equation in R 1+1 is in general ill-posed in the critical space ˙ H 1/2 , and the Besov space ˙ B 1/2,1 2. The problem is attributed to the bad behaviour of the one-dimensional bilinear expression D −1 (f Dg) in these spaces. 

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