On the Dirac delta as initial condition for nonlinear Schrödinger equations

Valeria Banica (1) , Luis Vega (2)

1 Département de Mathématiques (Evry)
2 UPV / EHU - University of the Basque Country = Euskal Herriko Unibertsitatea

In this article we will study the initial value problem for some Schrödinger equations with Diraclike initial data and therefore with infinite L2 mass, obtaining positive results for subcritical nonlinearities. In the critical case and in one dimension we prove that after some renormalization the corresponding solution has finite energy. This allows us to conclude a stability result in the defocusing setting. These problems are related to the existence of a singular dynamics for Schrödinger maps through the so called Hasimoto transformation.

Domaines: Equations aux dérivées partielles [math.AP]

Valeria Banica, Luis Vega. On the Dirac delta as initial condition for nonlinear Schrödinger equations. 2007. ⟨hal-00152299⟩