### Abstract

This paper proves the global existence of small radially symmetric solutions to the nonlinear Schrödinger equations of the form (i∂_{t}u + 1/2Δu = F(u,∇u, u,∇u), (t, x) ∈ R x R^{n}, u(0, x) = ε_{0}Φ(|x|), x ∈ R^{n}, where n ≥ 3, ∈0 is sufficiently small, |x| = with λ_{α},λ_{α,β} l_{1}, l_{2}, l_{3} ∈ N, l_{0} = 3 for n = 3, 4, and l_{0} = 2 for n ≥ 5. The method depends on the combination of a gauge transformation and generalized energy estimtes and does not require the condition such that ∂_{∇u}F is pure imaginary which is needed for the classical energy method.

Original language | English |
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Pages (from-to) | 1061-1072 |

Number of pages | 12 |

Journal | Differential and Integral Equations |

Volume | 8 |

Issue number | 5 |

Publication status | Published - 1995 |

Externally published | Yes |

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

Hayashi, N., Ozawa, T., & Temam, R. (1995). Global, small radially symmetric solutions to nonlinear Schrödinger equations and a gauge transformation.

*Differential and Integral Equations*,*8*(5), 1061-1072.