Publication Date

2003

Journal or Book Title

Communications on Pure and Applied Mathematics

Abstract

We study the question of well-posedness of the Cauchy problem for Schr¨odinger maps from R 1 ×R 2 to the sphere S 2 or to H2 , the hyperbolic space. The idea is to choose an appropriate gauge change so that the derivatives of the map will satisfy a certain nonlinear Schr¨odinger system of equations and then study this modified Schr¨odinger map system (MSM). We then prove local well posedness of the Cauchy problem for the MSM with minimal regularity assumptions on the data and outline a method to derive well posedness of the Schr¨odinger map itself from it. In proving well posedness of the MSM, the heart of the matter is resolved by considering truly quatrilinear forms of weighted L 2 functions.

Comments

This article was harvested from arXiv.

Publisher's version is here: http://onlinelibrary.wiley.com/doi/10.1002/cpa.10054/full

DOI: 10.1002/cpa.10054

Pages

114-151

Volume

56

Issue

1

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