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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 shows that earlier results of Bethuel-Saut for data of the form 1 + H 1 and Gérard for finite energy data remain true for this class of rough data.

Unconditional global well-posedness for the 3D Gross-Pitaevskii equation for data without finite energy