Global well-posedness for 2D radial Schrödinger maps into the sphere

Abstract

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

17 pages

References in corpus (3)

• Blow up dynamics for smooth data equivariant solutions to the energy critical Schrodinger map problem
• Global Schrödinger maps
• Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems