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Izvestiya: Mathematics, 2009, Volume 73, Issue 3, Pages 555–577
DOI: https://doi.org/10.1070/IM2009v073n03ABEH002456 (Mi im2671) 		 
This article is cited in 6 scientific papers (total in 6 papers)

A sharp constant in a Sobolev–Nirenberg inequality and its application to the Schrödinger equation

Sh. M. Nasibov

Institute of Applied Mathematics, Baku State University
English version PDF (406 kB) Citations (6) Russian version article
References:
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DOI: https://doi.org/10.1070/IM2009v073n03ABEH002456
Abstract: We prove that the solution of the Cauchy problem for a non-linear Schrödinger evolution equation with critical and supercritical exponents can blow up at a finite time for some initial data, and this time is estimated from above and below. To this end, an interpolation Nirenberg-type inequality and a Sobolev-type inequality are proved and the values of sharp constants in these inequalities are calculated.
Keywords: Nirenberg–Sobolev inequality, sharp constant, non-linear Schrödinger equation, blow-up, global solubility.
Received: 01.06.2007
Revised: 29.02.2008
Bibliographic databases:
UDC: 517.946.51.9
MSC: Primary 35J10; Secondary 35Q55, 46E35, 74H35
Language: English
Original paper language: Russian
Citation: Sh. M. Nasibov, “A sharp constant in a Sobolev–Nirenberg inequality and its application to the Schrödinger equation”, Izv. Math., 73:3 (2009), 555–577
Citation in format AMSBIB
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\paper A sharp constant in a Sobolev--Nirenberg inequality and its application to the Schr\"odinger equation
\jour Izv. Math.
\yr 2009
\vol 73
\issue 3
\pages 555--577
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  • https://doi.org/10.1070/IM2009v073n03ABEH002456
  • https://www.mathnet.ru/eng/im/v73/i3/p127
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:671
    Russian version PDF:237
    English version PDF:35
    References:95
    First page:13
     
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