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Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/25689

Title: BOOTSTRAPPED MORAWETZ ESTIMATES AND RESONANT DECOMPOSITION FOR LOW REGULARITY GLOBAL SOLUTIONS OF CUBIC NLS ON \(R^2\)
Authors: Colliander, James
Roy, Tristan
Keywords: Nonlinear Schrodinger
bootstraps
interaction Morawetz
scattering
global well-posedness
Issue Date: Mar-2011
Publisher: AIM Sciences
Citation: Communcations on Pure and Applied analysis, v. 10, no. 2, pp 397--414
Abstract: We prove global well-posedness for the \(L^2\)-critical cubic defocusing nonlinear Schr odinger equation on \(R^2\) with data \(u_0 \in H^s( R^2)\) for \(s > \frac{1}{3}\) . The proof combines a priori Morawetz estimates obtained and the improved almost conservation law obtained in earlier works. There are two technical di culties. The firrst one is to estimate the variation of the improved almost conservation law on intervals given in terms of Strichartz spaces rather than in terms of \(X^{s,b}\) spaces. The second one is to control the error of the a priori Morawetz estimates on an arbitrary large time interval, which is performed by a bootstrap via a double layer in time decomposition.
URI: http://hdl.handle.net/1807/25689
Appears in Collections:Department of Mathematics

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