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Blowup results for the fractional Schrödinger equation without gauge invariance

  • *Corresponding author: Qihong Shi

    *Corresponding author: Qihong Shi 

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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  • 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.

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


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