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

Nakao Hayashi; Tohru Ozawa

doi:10.1007/BF01212423

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

Nakao Hayashi, Tohru Ozawa

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

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	https://doi.org/10.1007/BF01212423
Publication status	Published - 1987 Sep 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01212423

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title = "Time decay of solutions to the cauchy problem for time-dependent Schr{\"o}dinger-Hartree equations",

abstract = "We consider the time-dependent Schr{\"o}dinger-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}",

author = "Nakao Hayashi and Tohru Ozawa",

year = "1987",

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doi = "10.1007/BF01212423",

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AU - Hayashi, Nakao

AU - Ozawa, Tohru

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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}

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

Abstract

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