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 4, 2012.
Math Subject Classifications: 35Q55, 35B60, 37L50.
Key Words: Gross-Pitaevskii equation; global well-posedness; Fourier restriction norm method.
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| Hartmut Pecher |
Fachbereich Mathematik und Naturwissenschaften
Bergische Universität Wuppertal
Gaussstr. 20, 42097 Wuppertal, Germany
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