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

Terence Tao

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arXiv · math/9811169

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

Terence Tao

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Abstract

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.

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Terence Tao. 1999-03-29. Ill-posedness for one-dimensional wave maps at the critical regularity. https://arxiv.org/abs/math/9811169

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