Hyperboloidal evolution and global dynamics for the focusing cubic wave equation

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