We consider the focusing mass-critical NLS
in high dimensions
, with initial
data
having
finite mass
.
It is well known that this problem admits unique (but not global) strong solutions in the
Strichartz class
,
and also admits global (but not unique) weak solutions in
. In this
paper we introduce an intermediate class of solution, which we call a
semi-Strichartzclass solution, for which one does have global existence and uniqueness in dimensions
. In
dimensions
and assuming spherical symmetry, we also show the equivalence of the Strichartz
class and the strong solution class (and also of the semi-Strichartz class and the
semi-strong solution class), thus establishing
unconditional uniqueness results in the
strong and semi-strong classes. With these assumptions we also characterise
these solutions in terms of the continuity properties of the mass function
.
