Mathematics – Analysis of PDEs
Scientific paper
2005-12-01
Mathematics
Analysis of PDEs
Scientific paper
In this paper we consider the local well-posedness theory for the quadratic
nonlinear Schr\"odinger 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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