Abstract
This work considers the long time behavior of the solutions
u
∈
C
(
R
,
H
1
)
to the attractive Hartree equation
i
u
˙
+
Δ
u
=
(
I
α
∗
|
⋅
|
−
γ
|
u
|
p
)
|
x
|
−
γ
|
u
|
p
−
2
u
.
Indeed, using a classical Morawetz estimate, the scattering of radial global solutions is proved in
L
2
-super-critical and
H
1
-sub-critical regimes.