Scattering of the energy-critical NLS with dipolar interaction

Abstract

In this paper, we investigate the global well-posedness and $H^1$ scattering theory for a 3d energy-critical Schrödinger equation under the influence of magnetic dipole interaction ${\lambda }_1|u{|}^{2}u+{\lambda }_2(K\ast |u{|}^2)u$, where $K$ is the dipole-dipole interaction kernel. Our proof of global well-posedness result is based on the argument of Zhang [23]. Moreover, adopting the induction of energy technique of Killip-Oh-Pocovnicu-Visan [20], we obtain a condition for scattering.

arXiv comment33 pages

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