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Zbl 1122.35132
Fang, Y.F.; Grillakis, Manoussos G.
On the global existence of rough solutions of the cubic defocusing Schrödinger equation in $\Bbb R^{2 + 1}$.
(English)
[J] J. Hyperbolic Differ. Equ. 4, No. 2, 233-257 (2007). ISSN 0219-8916

Authors' abstract: We consider the cubic defocusing Schrödinger equation in two space dimensions and prove that if the initial data are in $H^{1/2}$, then there exists a global solution in time. The proof combines the argument from [{\it J. Colliander, M. Keel, G. Staffilani, H. Takaoka} and {\it T. Tao}, Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, preprint] with some new correlation estimates for the Schrödinger equation.
[A. D. Osborne (Keele)]
MSC 2000:
*35Q55 NLS-like (nonlinear Schroedinger) equations
35L40 First order hyperbolic systems, general
76N10 Compressible fluids, general

Keywords: I-method; Strichartz estimates; correlation estimates; conservation laws

Cited in: Zbl 1142.35085

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