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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 209, Number 3, Pages 427–437
DOI: https://doi.org/10.4213/tmf10134 (Mi tmf10134) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Nonlinear evolutionary Schrödinger equation in the supercritical case

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan
Full-text PDF (452 kB) Citations (2)
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DOI: https://doi.org/10.4213/tmf10134
Abstract: We prove that for some initial data, solutions of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case are destroyed after a finite time, the exact value of which can be estimated from above. Lower bounds are obtained for the rate of destruction of the solution in some norms. A set of initial data is identified for which the solution of the Cauchy problem for the nonlinear Schrödinger equation in the supercritical case exists globally.
Keywords: nonlinear evolutionary Schrödinger equation, Cauchy problem, solution blow-up, blow-up rate, interpolation inequality, global solvability.
Received: 09.06.2021
Revised: 09.06.2021
English version:
Theoretical and Mathematical Physics, 2021, Volume 209, Issue 3, Pages 1683–1692
DOI: https://doi.org/10.1134/S0040577921120035
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Sh. M. Nasibov, “Nonlinear evolutionary Schrödinger equation in the supercritical case”, TMF, 209:3 (2021), 427–437; Theoret. and Math. Phys., 209:3 (2021), 1683–1692
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v209/i3/p427
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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