Abstract
This note studies the Choquard equation with exponential source term in two space dimensions:
i
u
˙
+
Δ
u
=
ϵ
(
I
α
∗
G
(
|
u
|
2
)
)
g
(
u
)
.
First, the local/global well-posedness and scattering are obtained in the energy space. Second, the existence of unstable standing waves is proved. Finally, the existence of global/non-global solutions is discussed via the potential-well method.