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

Terence Tao

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

偏微分方程分析 2007-05-23 v2

作者: Terence Tao

摘要

We show that the wave map equation in $\R^{1+1}$ is in general ill-posed in the critical space $\dot H^{1/2}$ , and the Besov space $\dot B^{1/2,1}_2$ . The problem is attributed to the bad behaviour of the one-dimensional bilinear expression $D^{-1}(f Dg)$ in these spaces.

引用

@article{arxiv.math/9811169,
  title  = {Ill-posedness for one-dimensional wave maps at the critical regularity},
  author = {Terence Tao},
  journal= {arXiv preprint arXiv:math/9811169},
  year   = {2007}
}

备注

10 pages, 1 figure, submitted to Amer. J. Math

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