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arXiv · 1207.1087

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

Hartmut Pecher
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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.

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Hartmut Pecher. 2012-10-05. Global solutions for 3D nonlocal Gross-Pitaevskii equations with rough data. https://arxiv.org/abs/1207.1087

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