Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 170, pp. 1-34.

Title: Global solutions for 3D nonlocal Gross-Pitaevskii 
       equations with rough data

Author: Hartmut Pecher (Bergische Univ., Wuppertal, Germany)

Abstract:
 We study the Cauchy problem for the Gross-Pitaevskii equation with a nonlocal
 interaction potential of Hartree type in three space dimensions.
 If the potential is even and positive definite or a positive function and
 its Fourier transform decays sufficiently rapidly the problem is shown to
 be globally well-posed for large rough data which not necessarily have
 finite energy and also in a situation where the energy functional is not
 positive definite. The proof uses a suitable modification of the I-method.

Submitted July 6, 2012. Published October 04, 2012.
Math Subject Classifications: 35Q55, 35B60, 37L50.
Key Words: Gross-Pitaevskii equation; global well-posedness;
           Fourier restriction norm method.