For the critical focusing wave equation on in the radial case, we establish the role of the “center stable” manifold constructed in [18] near the ground state as a threshold between blowup and scattering to zero, establishing a conjecture going back to numerical work by Bizo´n, Chmaj, Tabor [3]. The underlying topology is stronger than the energy norm.
Giovanni De Micheli, Luca Benini, Srinivasan Murali, Federico Angiolini, Hamid Sarbazi-Azad, Dara Rahmati