Speaker: Jessica Trespalacios
DIM – Universidad de Chile

Date:  March 29, 2022 at 12 Santiago time

Abstract: We consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally, some applications are presented in the case of PCF solitons, a first step towards the study of its nonlinear stability.

Venue: Online via Zoom / Sala de seminarios DIM, Beauchef 851, piso 5
Chair: Hanne Van Den Bosch