For the critical focusing wave equation $\Box u = u^5$ on $\R^{ 3+1}$ in the radial case, we establish the role of the "center stable" manifold $\Sigma$ constructed in \cite{ KS} near the ground state $(W,0)$ as a threshold between type I blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo\'n, Chmaj, Tabor. The underlying topology is stronger than the energy norm.
Categories: math.AP