Equivariant Schrödinger maps from two dimensional hyperbolic space

Abstract

In this article, we consider the equivariant Schrödinger map from ${\mathbb{H}}^2$ to ${\mathbb{S}}^2$ which converges to the north pole of ${\mathbb{S}}^2$ at the origin and spatial infinity of the hyperbolic space. If the energy of the data is less than $4\pi$, we show that the local existence of Schrödinger map. Furthermore, if the energy of the data sufficiently small, we prove the solutions are global in time.

References in corpus (3)

• Dispersive Estimates for Scalar and Matrix Schrödinger operators on ${\mathbb{H}}^{n+1}$
• Asymptotic stability of harmonic maps between 2D hyperbolic spaces under the wave map equation. II. Small energy case
• Convergence to harmonic maps for the Landau-Lifshitz flows on two dimensional hyperbolic spaces