Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity
arXiv:0907.5227 · doi:10.1080/03605302.2010.497200
Abstract
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.
Communications in Partial Differential Equations (2010)
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