Hyperboloidal Evolution and Global Dynamics for the Focusing Cubic Wave Equation

The focusing cubic wave equation in three spatial dimensions has the explicit solution 2 / t . We study the stability of the blowup described by this solution as t → 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 2 / t as t → ∞ . These global solutions thus exhibit a slow nondispersive decay, in contrast to small data evolutions.