Equivariant Schrödinger Maps in two spatial dimensions

Abstract

We consider equivariant solutions for the Schrödinger map problem from ${\mathbb{R}}^{2+1}$ to ${\mathbb{S}}^2$ with energy less than $4\pi$ and show that they are global in time and scatter.

References in corpus (3)

• Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrodinger equation in the radial case
• Global results for Schrödinger Maps in dimensions $n\ge 3$
• Low-regularity Schrödinger maps, II: global well-posedness in dimensions $d\ge 3$

Cited by in corpus (12)

• On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy
• On energy-critical half-wave maps into ${\mathbb{S}}^2$
• Equivariant Schrödinger Maps in two spatial dimensions: the $\H^2$ target
• Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: Energy critical case
• Local well-posedness for the Landau-Lifshitz equation with helicity term
• Global Schrödinger map flows to Kähler manifolds with small data in critical Sobolev spaces: High dimensions
• Bilinear Strichartz estimates for the Schr{ö}dinger map problem
• Phase transition threshold and stability of magnetic skyrmions
• Asymptotic behaviors of Landau-Lifshitz flows from ${\mathbb{R}}^2$ to Kähler manifolds
• Blowup dynamics for smooth equivariant solutions to energy critical Landau-Lifschitz flow
• On long time dynamics of 1D Schrödinger map flows
• On Threshold Solutions of equivariant Chern-Simons-Schrödinger Equation