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International Mathematics Research Papers (2006) Vol. 2006 : article ID 70630, 84 pages, doi:10.1155/IMRP/2006/70630
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Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.

Quadratic nonlinear derivative Schrödinger equations. Part I

Ioan Bejenaru

Department of Mathematics, University of California, Los Angeles (UCLA) Los Angeles, CA 90095-1555, USA E-mail address: bejenaru{at}math.ucla.edu

We consider the local well-posedness theory for the quadratic nonlinear Schrödinger equation with low regularity initial data in the case when the nonlinearity contains derivatives. We work in 2 + 1 dimensions and prove a local well-posedness result up to the scaling for small initial data with some spherical symmetry structure.


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