Global well-posedness for 2D radial Schr\"odinger maps into the sphere

Stephen Gustafson; Eva Koo

Global well-posedness for 2D radial Schr\"odinger maps into the sphere

Analysis of PDEs 2011-05-31 v1

Authors: Stephen Gustafson , Eva Koo

Abstract

We prove global well-posedness for a cubic, non-local Schr\"odinger equation with radially-symmetric initial data in the critical space $L^2(\R^2)$ , using the framework of Kenig-Merle and Killip-Tao-Visan. As a consequence, we obtain a global well-posedness result for Schr\"odinger maps from $\R^2$ into $\S^2$ (Landau-Lifshitz equation) with radially symmetric initial data (with no size restriction).

Keywords

global well-posedness schrödinger map radial symmetry critical space landau-lifshitz equation kenig-merle framework

Cite

@article{arxiv.1105.5659,
  title  = {Global well-posedness for 2D radial Schr\"odinger maps into the sphere},
  author = {Stephen Gustafson and Eva Koo},
  journal= {arXiv preprint arXiv:1105.5659},
  year   = {2011}
}

Comments

17 pages

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