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Low regularity solutions for a 2D quadratic nonlinear Schrödinger equation

Authors:	Ioan Bejenaru Daniela De Silva

Institution:	Department of Mathematics, University of California, Los Angeles, California 90095 ; Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218

Abstract:	We establish that the initial value problem for the quadratic non-linear Schrödinger equation $\displaystyle iu_t - \Delta u = u^2,$ where $u: \mathbb{R}^2 \times \mathbb{R} \to \mathbb{C}$ , is locally well-posed in $H^s(\mathbb{R}^2)$ when . The critical exponent for this problem is , and previous work by Colliander, Delort, Kenig and Staffilani, 2001, established local well-posedness for .

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