Unconditional global well-posedness for the 3D Gross-Pitaevskii equation   for data without finite energy
  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. 
Hartmut Pecher
math.AP