On the Dirac delta as initial condition for nonlinear Schrödinger equations

Details On the Dirac delta as initial condition for nonlinear Schrödinger equations On the Dirac delta as initial condition for nonlinear Schrödinger equations

2007-06-06

arxiv.org/abs/0706.0819v1

Mathematics

Analysis of PDEs

17 pages, to appear in in AnIHP Ann Non Lin

Scientific paper

In this article we will study the initial value problem for some Schr\"odinger 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 Schr\"odinger maps through the so called Hasimoto transformation.

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