## Abstract

We consider the initial value problem for nonlinear Schrödinger equations with the critical nonlinearities λ1|u|^{2/n}u, where Imλ_{1}≤0, when the space dimension n=1, 2. We prove the global existence of small solutions in homogeneous weighted L^{2}(R^{n}) spaces. It is shown that the small solutions decay uniformly like t^{-n/2} for t>1 if Imλ_{1}=0. The higher uniform time decay rates t-n2(logt)-n2 for t>1 are obtained if Imλ_{1}<0.

Original language | English |
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Pages (from-to) | 1214-1234 |

Number of pages | 21 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 419 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 Nov 15 |

Externally published | Yes |

## Keywords

- Critical nonlinearities
- Nonlinear Schrödinger equations

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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