TITLE:
Global Existence and Finite Time Blow-Up for the Nonlinear Schrödinger Hartree Equation with a Constant Magnetic Field
AUTHORS:
Fangli Zhou
KEYWORDS:
Nonlinear Schrödinger Hartree Equation, Global Existence, Finite-Time Blow-Up
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
March
30,
2026
ABSTRACT: The paper addresses the global existence and finite-time blow-up phenomena for the nonlinear Schrödinger Hartree equation in the presence of a constant magnetic field, which is given by:
i
∂
t
ψ+
(
∇+iA
)
2
ψ−(
| x |
−1
∗
| ψ |
2
)ψ+
| ψ |
p
ψ=0
,
(
t,x
)∈
ℝ
+
×
ℝ
3
. This equation is considered in three-dimensional space. Under mass-critical and supercritical conditions, we determine the precise thresholds for global existence and finite-time blow-up in the
L
2
-supercritical regime, specifically for the range
4
3