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 |
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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.
In: Communications in Mathematical Physics, Vol. 110, No. 3, 09.1987, p. 467-478.Research output: Contribution to journal › Article
}
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 -