### Abstract

We consider the time-dependent Schrödinger-Hartree equation {Mathematical expression} {Mathematical expression} where λ≧0 and {Mathematical expression}. We show that there exists a unique global solution u of (1) and (2) such that {Mathematical expression} with {Mathematical expression} Furthermore, we show that u has the following estimates: {Mathematical expression} and {Mathematical expression}

Original language | English |
---|---|

Pages (from-to) | 467-478 |

Number of pages | 12 |

Journal | Communications in Mathematical Physics |

Volume | 110 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1987 Sep |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

**Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations.** / Hayashi, Nakao; Ozawa, Tohru.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 110, no. 3, pp. 467-478. https://doi.org/10.1007/BF01212423

}

TY - JOUR

T1 - Time decay of solutions to the cauchy problem for time-dependent Schrödinger-Hartree equations

AU - Hayashi, Nakao

AU - Ozawa, Tohru

PY - 1987/9

Y1 - 1987/9

N2 - We consider the time-dependent Schrödinger-Hartree equation {Mathematical expression} {Mathematical expression} where λ≧0 and {Mathematical expression}. We show that there exists a unique global solution u of (1) and (2) such that {Mathematical expression} with {Mathematical expression} Furthermore, we show that u has the following estimates: {Mathematical expression} and {Mathematical expression}

AB - We consider the time-dependent Schrödinger-Hartree equation {Mathematical expression} {Mathematical expression} where λ≧0 and {Mathematical expression}. We show that there exists a unique global solution u of (1) and (2) such that {Mathematical expression} with {Mathematical expression} Furthermore, we show that u has the following estimates: {Mathematical expression} and {Mathematical expression}

UR - http://www.scopus.com/inward/record.url?scp=0039582645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039582645&partnerID=8YFLogxK

U2 - 10.1007/BF01212423

DO - 10.1007/BF01212423

M3 - Article

AN - SCOPUS:0039582645

VL - 110

SP - 467

EP - 478

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -