On Schrödinger Maps

Abstract

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

References in corpus (2)

• Global regularity of wave maps II. Small energy in two dimensions
• Quadratic Nonlinear Derivative Schrödiger Equations - Part 1

Cited by in corpus (13)

• Global results for Schrödinger Maps in dimensions $n\ge 3$
• The initial value problem for a third-order dispersive flow into compact almost Hermitian manifolds
• Global Schrödinger maps
• Sharp global well-posedness for non-elliptic derivative Schrödinger equations with small rough data
• Low-regularity Schrödinger maps, II: global well-posedness in dimensions $d\ge 3$
• Global regularity of critical Schrödinger maps: subthreshold dispersed energy
• An unconstrained Lagrangian formulation and conservation laws for the Schrödinger map system
• The inviscid limit for the Landau-Lifshitz-Gilbert equation in the critical Besov space
• Global Well-Posedness of the Landau-Lifshitz-Gilbert equation for initial data in Morrey space
• Equivariant and self-similar standing waves for a Hamiltonian hyperbolic-hyperbolic spin-field system
• Low-regularity Schrödinger maps
• Global existence and uniqueness of Schrödinger maps in dimensions $d\ge 4$
• Very regular solution to Landau-Lifshitz system with spin-polarized transport