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The focusing cubic wave equation in three spatial dimensions has the explicitsolution $\sqrt{2}/t$. We study the stability of the blowup described by thissolution as $t \to 0$ without symmetry restrictions on the data. Via theconformal invariance of the equation we obtain a companion result for thestability of slow decay in the framework of a hyperboloidal initial valueformulation. More precisely, we identify a codimension-1 Lipschitz manifold ofinitial data leading to solutions which converge to Lorentz boosts of$\sqrt{2}/t$ as $t\to\infty$. These global solutions thus exhibit a slownondispersive decay, in contrast to small data evolutions.

Hyperboloidal evolution and global dynamics for the focusing cubic wave equation