Threshold phenomenon for the quintic wave equation in three dimensions

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 $Σ$ 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 Bizoń, Chmaj, Tabor. The underlying topology is stronger than the energy norm.

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