TY - JOUR
T1 - Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation
AU - Tao , Lu
AU - Zhao , Yajuan
AU - Li , Yongsheng
JO - Journal of Partial Differential Equations
VL - 1
SP - 82
EP - 101
PY - 2022
DA - 2022/12
SN - 36
DO - http://doi.org/10.4208/jpde.v36.n1.6
UR - https://global-sci.org/intro/article_detail/jpde/21295.html
KW - Fractional Schrödinger equation, Hartree-type nonlinearity, well-posedness, blow-up.
AB - <p style="text-align: justify;">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.</p>