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 (5)

• Regularity of Wave-Maps in dimension 2+1
• Energy dispersed large data wave maps in 2+1 dimensions
• 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

Cited by in corpus (5)

• Global wellposedness of the equivariant Chern-Simons-Schrödinger equation
• Local well-posedness for the Landau-Lifshitz equation with helicity term
• Bilinear Strichartz estimates for the Schr{ö}dinger map problem
• Remarks on local theory for Schrödinger maps near harmonic maps
• Blow up dynamics for equivariant critical Schrödinger maps