Open AccessBlowup results for the fractional Schrödinger equation without gauge invariance
Author(s) -
Qinwei Shi,
Congming Peng,
Qingxuan Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021304
Subject(s) - mathematics , order (exchange) , space (punctuation) , operator (biology) , power function , arithmetic , combinatorics , mathematical analysis , computer science , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene , operating system
This paper is concerned with the nonexistence of global solutions to the fractional Schrödinger equations with order \begin{document}$ \alpha $\end{document} and nongauge power type nonlinearity \begin{document}$ |u|^p $\end{document} for any space dimensions, where \begin{document}$ \alpha\in (0, 2] $\end{document} is assumed to be any fractional numbers. A modified test function is employed to overcome some difficulties caused by the fractional operator and to establish blowup results. Some restrictions with respect to \begin{document}$ \alpha, p $\end{document} and initial data in the previous literature are removed.