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Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance

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Fractional Calculus and Applied Analysis Aims and scope Submit manuscript

To Professor J. A. Tenreiro Machado, in Memoriam

Abstract

In this paper, we consider the Cauchy problem in \(\mathbb {R}^N\), \(N\ge 1\), for semi-linear Schrödinger equations with space–time fractional derivatives. We discuss the nonexistence of global \(L^1\) or \(L^2\) weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local \(L^1\) or \(L^2\) weak solutions in the supercritical case are studied.

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Acknowledgements

The second author is supported by the Lebanese University research program.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Khalifa University, P.O. Box: 127788, Abu Dhabi, United Arab Emirates

    Mokhtar Kirane

  2. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jidda, 21589, Saudi Arabia

    Mokhtar Kirane

  3. Department of Mathematics, Faculty of Sciences III, Lebanese University, P.O. Box 1352,, Tripoli, Lebanon

    Ahmad Z. Fino

  4. FracDiff Research Group (DR/RG/03), Department of Mathematics, Sultan Qaboos University, Al-Khoud, P.O. Box 46, 123, Muscat, Oman

    Ahmad Z. Fino

Authors
  1. Mokhtar Kirane
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  2. Ahmad Z. Fino
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Correspondence to Mokhtar Kirane.

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Kirane, M., Fino, A.Z. Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance. Fract Calc Appl Anal 25, 1361–1387 (2022). https://doi.org/10.1007/s13540-022-00046-y

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  • DOI: https://doi.org/10.1007/s13540-022-00046-y

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