![Spectral theory / Mathematics / Multivariable calculus / Partial differential equation / Wave equation / Mathematical analysis / Operator theory / Ordinary differential equations Spectral theory / Mathematics / Multivariable calculus / Partial differential equation / Wave equation / Mathematical analysis / Operator theory / Ordinary differential equations](https://www.pdfsearch.io/img/ef22cef502d0a13be81b9b67ac7329a8.jpg) Date: 2009-11-15 22:14:44Spectral theory Mathematics Multivariable calculus Partial differential equation Wave equation Mathematical analysis Operator theory Ordinary differential equations | | BLOW-UP CRITERIA FOR THE 3D CUBIC NONLINEAR ¨ SCHRODINGER EQUATION JUSTIN HOLMER, RODRIGO PLATTE, AND SVETLANA ROUDENKO Abstract. We consider solutions u to the 3d nonlinear Schr¨odinger equation i∂t u+
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