  The Cauchy problem for the Gross-Pitaevskii equation in three space
dimensions is shown to have an unconditionally unique global solution for data
of the form 1 + H^s for 5/6 < s < 1, which do not have necessarily finite
energy. The proof uses the I-method which is complicated by the fact that no
L^2 -conservation law holds. This improves former results of Bethuel-Saut and
Gerard.
