Local well-posedness for hyperbolic-elliptic Ishimori equation

Details Local well-posedness for hyperbolic-elliptic Ishimori equation Local well-posedness for hyperbolic-elliptic Ishimori equation

2009-08-27

arxiv.org/abs/0908.4018v1

Mathematics

Analysis of PDEs

30 pages

Scientific paper

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.

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