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Sbornik: Mathematics, 2009, Volume 200, Issue 4, Pages 549–572
DOI: https://doi.org/10.1070/SM2009v200n04ABEH004008 (Mi sm6365) 		 
This article is cited in 26 scientific papers (total in 26 papers)

Blow-up of Oskolkov's system of equations

M. O. Korpusov, A. G. Sveshnikov

M. V. Lomonosov Moscow State University, Faculty of Physics
English version PDF (368 kB) Citations (26)
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DOI: https://doi.org/10.1070/SM2009v200n04ABEH004008
Abstract: Oskolkov's system of equations with a cubic source is considered; this describes the dynamics of a viscoelastic fluid. Local solvability (with respect to time) of the problem in the weak generalized sense is proved. Some conditions on the initial function which ensure that the solution blows up in finite time are found, and two-sided estimates for the existence time of the solution are obtained. Moreover, sufficient conditions for the global solvability (with respect to time) of the problem are found.
Bibliography: 19 titles.
Keywords: blow-up for Oskolkov's system of equations, generalized solution, equations of hydrodynamic type.
Received: 21.05.2008 and 21.11.2008
Russian version:
Matematicheskii Sbornik, 2009, Volume 200, Number 4, Pages 83–108
DOI: https://doi.org/10.4213/sm6365
Bibliographic databases:
UDC: 517.957
MSC: 76A10, 35Q35, 76D03
Language: English
Original paper language: Russian
Citation: M. O. Korpusov, A. G. Sveshnikov, “Blow-up of Oskolkov's system of equations”, Mat. Sb., 200:4 (2009), 83–108; Sb. Math., 200:4 (2009), 549–572
Citation in format AMSBIB
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    • This publication is cited in the following 26 articles:
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