full
search.png

Search

close.png

Cancel

arrow
Volume 36, Issue 1
Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation

Lu Tao, Yajuan Zhao & Yongsheng Li

DOI: 10.4208/jpde.v36.n1.6

J. Part. Diff. Eq., 36 (2023), pp. 82-101.

Published online: 2022-12

Preview Full PDF 2183 30110

Cited by

google scholar semantic scholar
Export citation
  • 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.

  • Keywords

Fractional Schrödinger equation, Hartree-type nonlinearity, well-posedness, blow-up.

  • AMS Subject Headings

35R11, 35B44, 35A01, 35Q55

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

taolu1998@126.com (Lu Tao)

zhaoyj_91@163.com (Yajuan Zhao)

yshli@scut.edu.cn (Yongsheng Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-36-82, author = {Tao , LuZhao , Yajuan and Li , Yongsheng}, title = {Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {36}, number = {1}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v36.n1.6}, url = {http://global-sci.org/intro/article_detail/jpde/21295.html} }
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 -

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.

Tao , LuZhao , Yajuan and Li , Yongsheng. (2022). Well-Posedness and Blow-Up for the Fractional Schrödinger-Choquard Equation. Journal of Partial Differential Equations. 36 (1). 82-101. doi:10.4208/jpde.v36.n1.6
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard