Blowup results for the fractional Schrödinger equation without gauge invariance

Qihong Shi; Congming Peng; Qingxuan Wang

doi:10.3934/dcdsb.2021304

Article Contents

2022, Volume 27, Issue 10: 6009-6022. Doi: 10.3934/dcdsb.2021304

This issue Previous Article Continuity of random attractors on a topological space and fractional delayed FitzHugh-Nagumo equations with WZ-noise Next Article On the well-posedness of the anisotropically-reduced two-dimensional Kuramoto-Sivashinsky Equation

Blowup results for the fractional Schrödinger equation without gauge invariance

1.
Department of Mathematics, Lanzhou University of Technology, Lanzhou, 730050, China
2.
School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741001, China
3.
Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

^*Corresponding author: Qihong Shi
^*Corresponding author: Qihong Shi

Received: July 31, 2021

Early access: December 2021

Published: October 2022

The authors are supported by NNSF of China (Nos.12061040, 11701244, 11901266), NSF of Gansu Province of China(Nos. 20JR5RA460, 20JR5RA498) and the Innovation Ability Promotion Foundation of Universities in Gansu Province, China(No. 2020B-185)

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Abstract

This paper is concerned with the nonexistence of global solutions to the fractional Schrödinger equations with order $ \alpha $ and nongauge power type nonlinearity $ |u|^p $ for any space dimensions, where $ \alpha\in (0, 2] $ 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 $ \alpha, p $ and initial data in the previous literature are removed.

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Mathematics Subject Classification: Primary: 35Q55, 35R11; Secondary: 35B44.

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