On the Dirac delta as initial condition for nonlinear Schrodinger equations

In this article we will study the initial value problem for some Schrodinger equations with Dirac-like initial data and therefore with infinite L-2 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 Schrodinger maps through the so-called Hasimoto transformation. (C) 2007 Elsevier Masson SAS. All rights reserved.