Abstract
Abstract
We consider the radial nonlinear Schrödinger equation i∂
t
u + Δu = |u|
p−1
u in dimension d ⩾ 2 for
p
∈
1
,
1
+
4
d
and construct a natural Gaussian measure μ
0 which support is almost
L
rad
2
and such that μ
0—almost every initial data gives rise to a unique global solution. Furthermore, for
1+\frac{2}{d}$?>
p
>
1
+
2
d
and d ⩽ 10, the solutions constructed scatter in a space which is almost L
2. This paper can be viewed as a higher dimensional counterpart of the work of Burq and Thomann (2020 arXiv:2012.13571), in the radial case.
Subject
Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics