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Mat. Zametki, 2014, Volume 95, Issue 4, Pages 615–629 (Mi mz10241)  

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

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.

DOI: https://doi.org/10.4213/mzm10241

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English version:
Mathematical Notes, 2014, 95:4, 552–564

Bibliographic databases:

UDC: 517.958+539.3
Received: 30.01.2013

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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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Korpusov M. Ovchinnikov A. Sveshnikov A. Yushkov E., “Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods”, Blow-Up in Nonlinear Equations of Mathematical Physics: Theory and Methods, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter Gmbh, 2018, 1–326  crossref  isi
  • Математические заметки Mathematical Notes
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