Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

Details Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

2009-07-30

arxiv.org/abs/0907.5227v2

Mathematics

Analysis of PDEs

Communications in Partial Differential Equations (2010)

Scientific paper

10.1080/03605302.2010.497200

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.

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