From an Initial Data to a Global Solution of the Non-linear Schrödinger Equation: A Building Process

Abstract

The purpose of this work is to construct a continuous map from the homogeneous Besov space |$\dot B^0_{2,4}({\mathbb {R}}^2)$| in the set |$\mathcal {G}$| of initial data in |$\dot B^0_{2,4}({\mathbb R}^2)$| which gives birth to global solution of the mass critical non-linear Schrödinger equation in the space |$L^4({\mathbb R}^{1+2})$|⁠. We use the fact that solutions of scale which are different enough almost do not interact; the main point is that we determine a condition about the size of the scale which depends continuously on the data.

Locations

• International Mathematics Research Notices - View
• CiteSeer X (The Pennsylvania State University) - View - PDF
• HAL (Le Centre pour la Communication Scientifique Directe) - View - PDF