Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation

Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation

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.

Author Details

Lü Tao

Yajuan Zhao

Yongsheng Li