2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77774We 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.10 pages, 1 figure, submitted to Amer. J. MathAnalysis of PDEs35L70text