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On the global existence of rough solutions of the cubic defocusing Schrödinger equation in 2+1 . (English) Zbl 1122.35132
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 [J. Colliander, M. Keel, G. Staffilani, H. Takaoka and T. Tao, Almost conservation laws and global rough solutions to a nonlinear Schrödinger equation, preprint] with some new correlation estimates for the Schrödinger equation.

MSC:
35Q55NLS-like (nonlinear Schrödinger) equations
35L40First order hyperbolic systems, general
76N10Compressible fluids, general