Παρασκευή 6 Νοεμβρίου 2020, 13.00 – 14.00. Η ομιλία θα γίνει ONLINE.
Ομιλητής: Αθανάσιος Χατζηκαλέας, Pierre and Marie Curie University (Paris 6)
Τίτλος: Time periodic solutions for the conformal cubic wave equation on the Einstein cylinder
Περίληψη: We consider the conformal wave equation on the Einstein cylinder with a defocusing cubic non-linearity for small rotationally symmetric initial data. This equation captures many key features of non-linear wave dynamics for a self-interacting conformally coupled scalar field in the four-dimensional Anti-de Sitter spacetime and its stability conjecture. Motivated by a method developed for the spherically symmetric Einstein- Klein-Gordon system, we study perturbations around the zero solution as a formal series expansion and assume that the perturbations bifurcate from one mode. In the center of this work stands a rigorous proof on how one can choose the initial data to cancel out all secular terms in the resonant system. Interestingly, our analysis reveals that the only possible choice for the existence of time periodic solutions is when the error terms in the expansion are all proportional to the dominant one mode.