Year: 2023
Author: Lü Tao, Yajuan Zhao, Yongsheng Li
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 82–101
Abstract
In this paper, we study the well-posedness and blow-up solutions for the fractional Schrödinger equation with a Hartree-type nonlinearity together with a power-type subcritical or critical perturbations. For nonradial initial data or radial initial data, we prove the local well-posedness for the defocusing and the focusing cases with subcritical or critical nonlinearity. We obtain the global well-posedness for the defocusing case, and for the focusing mass-subcritical case or mass-critical case with initial data small enough. We also investigate blow-up solutions for the focusing mass-critical problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v36.n1.6
Journal of Partial Differential Equations, Vol. 36 (2023), Iss. 1 : pp. 82–101
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Fractional Schrödinger equation Hartree-type nonlinearity well-posedness blow-up.