Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons

Autor:	Trespalacios, Jessica
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematical Physics
Druh dokumentu:	Working Paper
Popis:	In this paper, 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. Comment: 24 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.02683 Zobrazit plný text záznamu View this record from Arxiv