### 抜粋

We consider the global Cauchy problem for a system of Schrödinger equations with quadratic interaction. Two types of analytic smoothing effect for the solutions are formulated in the small data setting under the mass resonance condition. One is the usual analytic smoothing effect in space variables in terms of the generator of Galilei transforms. We prove the existence and uniqueness of global solutions which are analytic with respect to Galilei generators for sufficiently small data with exponential decay at infinity in space ℝ^{n} with n ≥ 3. The other is analytic smoothing effect in space-time variables in terms of generator of pseudo-conformal and Galilei transforms. We prove the existence and uniqueness of global solutions which are analytic with respect to pseudo-conformal and Galilei generators for sufficiently small data with exponential decay in ℝ^{4}. We also discuss the associated Lagrange structure.

元の言語 | English |
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記事番号 | 091513 |

ジャーナル | Journal of Mathematical Physics |

巻 | 56 |

発行部数 | 9 |

DOI | |

出版物ステータス | Published - 2015 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics