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

Mokhtar Kirane; Ahmad Z. Fino

doi:10.1007/s13540-022-00046-y

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

Mokhtar Kirane
, Ahmad Z. Fino

Mathematics

Lebanese University
Sultane Qaboos University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we consider the Cauchy problem in R^N, N≥ 1 , for semi-linear Schrödinger equations with space–time fractional derivatives. We discuss the nonexistence of global L¹ or L² weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local L¹ or L² weak solutions in the supercritical case are studied.

Original language	British English
Pages (from-to)	1361-1387
Number of pages	27
Journal	Fractional Calculus and Applied Analysis
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s13540-022-00046-y
State	Published - Aug 2022

Keywords

Fractional derivatives and integrals
Nonexistence of global solution
Schrödinger equations (primary)
Test function method

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@article{133b16d07ce24c238507396128bc86bc,

title = "Some nonexistence results for space–time fractional Schr{\"o}dinger equations without gauge invariance",

abstract = "In this paper, we consider the Cauchy problem in RN, N≥ 1 , for semi-linear Schr{\"o}dinger equations with space–time fractional derivatives. We discuss the nonexistence of global L1 or L2 weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local L1 or L2 weak solutions in the supercritical case are studied.",

keywords = "Fractional derivatives and integrals, Nonexistence of global solution, Schr{\"o}dinger equations (primary), Test function method",

author = "Mokhtar Kirane and Fino, \{Ahmad Z.\}",

note = "Funding Information: The second author is supported by the Lebanese University research program. Publisher Copyright: {\textcopyright} 2022, Diogenes Co.Ltd.",

year = "2022",

month = aug,

doi = "10.1007/s13540-022-00046-y",

language = "British English",

volume = "25",

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journal = "Fractional Calculus and Applied Analysis",

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T1 - Some nonexistence results for space–time fractional Schrödinger equations without gauge invariance

AU - Kirane, Mokhtar

AU - Fino, Ahmad Z.

PY - 2022/8

Y1 - 2022/8

N2 - In this paper, we consider the Cauchy problem in RN, N≥ 1 , for semi-linear Schrödinger equations with space–time fractional derivatives. We discuss the nonexistence of global L1 or L2 weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local L1 or L2 weak solutions in the supercritical case are studied.

AB - In this paper, we consider the Cauchy problem in RN, N≥ 1 , for semi-linear Schrödinger equations with space–time fractional derivatives. We discuss the nonexistence of global L1 or L2 weak solutions in the subcritical and critical cases under some conditions on the initial data and the nonlinear term. Furthermore, the nonexistence of local L1 or L2 weak solutions in the supercritical case are studied.

KW - Fractional derivatives and integrals

KW - Nonexistence of global solution

KW - Schrödinger equations (primary)

KW - Test function method

UR - https://www.scopus.com/pages/publications/85133091517

U2 - 10.1007/s13540-022-00046-y

DO - 10.1007/s13540-022-00046-y

M3 - Article

AN - SCOPUS:85133091517

SN - 1311-0454

VL - 25

SP - 1361

EP - 1387

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

IS - 4

ER -

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

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