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Matematicheskie Zametki, 2014, Volume 95, Issue 4, Pages 615–629
DOI: https://doi.org/10.4213/mzm10241 (Mi mzm10241) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Blow-Up in Systems with Nonlinear Viscosity

E. V. Yushkov

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm10241
Abstract: Sufficient conditions for the blow-up of solutions of the hydrodynamic systems proposed by Ladyzhenskaya in 1966 with nonlinear viscosity and exterior sources are obtained. Questions relating to local solvability and uniqueness are answered using the finite-dimensional Galerkin approximation method The energy method, which was first applied to hydrodynamic systems by Korpusov and Sveshnikov, is used to obtain estimates of the blow-up time and blow-up rate. The determining role of nonlinear exterior sources, not viscous or hydrodynamic nonlinearity, on the occurrence of the blow-up effect is shown.
Keywords: hydrodynamic system with nonlinear viscosity, blow-up of solutions, Navier–Stokes system, nonlinear source, energy method, Galerkin approximation method, Banach space, Gronwall–Bellman lemma.
Received: 30.01.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 4, Pages 552–564
DOI: https://doi.org/10.1134/S0001434614030274
Bibliographic databases:
Document Type: Article
UDC: 517.958+539.3
Language: Russian
Citation: E. V. Yushkov, “Blow-Up in Systems with Nonlinear Viscosity”, Mat. Zametki, 95:4 (2014), 615–629; Math. Notes, 95:4 (2014), 552–564
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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