Hartmut Pecher
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 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 email: pecher@math.uni-wuppertal.de |
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