Exact Results in Quantum Theory

We study the singularity formation for the focusing quadratic wave equation in the energy supercritical case, i.e., for d ≥ 7. We establish the existence of a new, non-trivial, self-similar blow-up solution u∗ in explicit form. For d = 9, we investigate the stability of u∗ without any symmetry assumptions on the initial data and show that there is a family of perturbations that leads to blow-up via u∗. In similarity coordinates, this family corresponds to a co-dimension one Lipschitz manifold modulo translation symmetries. This is a joint work with Birgit Sch ̈orkhuber and Irfan Glogic.

Link: https://us02web.zoom.us/j/87158764274?pwd=QTdydXd3K1N4Vnpoc094N1o4ZTVNZz09(Meeting ID: 871 5876 4274 Passcode: 438484)