Local well-posedness for hyperbolic-elliptic Ishimori equation

Abstract

In this paper we consider the hyperbolic-elliptic Ishimori initial-value problem. We prove that such system is locally well-posed for small data in $H^s$ level space, for $s>3/2$. The new ingredient is that we develop the methods of Ionescu and Kenig \cite{IK} and \cite{IK2} to approach the problem in a perturbative way.

30 pages

References in corpus (3)

• Global results for Schrödinger Maps in dimensions $n\ge 3$
• Global Schrödinger maps
• On the stability of certain spin models in 2+1 dimensions