Blowup results for the fractional Schrödinger equation without gauge invariance

Abstract

<p style='text-indent:20px;'>This paper is concerned with the nonexistence of global solutions to the fractional Schrödinger equations with order <inline-formula><tex-math id="M1">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula> and nongauge power type nonlinearity <inline-formula><tex-math id="M2">\begin{document}$ |u|^p $\end{document}</tex-math></inline-formula> for any space dimensions, where <inline-formula><tex-math id="M3">\begin{document}$ \alpha\in (0, 2] $\end{document}</tex-math></inline-formula> is assumed to be any fractional numbers. A modified test function is employed to overcome some difficulties caused by the fractional operator and to establish blowup results. Some restrictions with respect to <inline-formula><tex-math id="M4">\begin{document}$ \alpha, p $\end{document}</tex-math></inline-formula> and initial data in the previous literature are removed.</p>