We explore the long-time dynamics of the wave equation with conformally-invariant power nonlinearity on the Minkowski spacetime. In the focusing case, solutions can scatter to linear or blow-up in finite time. What is the *threshold* behaviour between these two? We prove that such behaviour is unstable. That is, given any solution that does not exhibit one of these two behaviours, we construct explicit, arbitrarily small perturbations to make it either scatter or blow-up. Further, we construct a rather explicit family of global solutions with such threshold behaviour, and we compare them to an interesting numerical conjecture due to Bizon and Zenginoglu.

à venir

à venir

à venir

à venir