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

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

1998-11-29

arxiv.org/abs/math/9811169v2

Mathematics

Analysis of PDEs

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

Scientific paper

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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