Global results for Schrödinger Maps in dimensions $n\ge 3$

Abstract

We study the global well-posedness theory for the Schrödinger Maps equation. We work in $n+1$ dimensions, for $n\ge 3$, and prove a local well-posedness for small initial data in ${\dot{B}}_{2,1}^{\frac{n}{2}}$.

The previous version had few gaps in the argument. The new version fixes them

References in corpus (2)

• Global regularity of wave maps II. Small energy in two dimensions
• On Schrödinger Maps

Cited by in corpus (8)

• Equivariant Schrödinger Maps in two spatial dimensions
• Global Schrödinger maps
• Sharp global well-posedness for non-elliptic derivative Schrödinger equations with small rough data
• Global regularity of critical Schrödinger maps: subthreshold dispersed energy
• Local well-posedness for hyperbolic-elliptic Ishimori equation
• Very regular solution to Landau-Lifshitz system with spin-polarized transport
• The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
• Global well-posedness for the Schrödinger map problem with small Besov norm