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Matematicheskie Zametki, 2007, Volume 82, Issue 1, Pages 135–149
DOI: https://doi.org/10.4213/mzm3761 (Mi mzm3761) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Variational Inequalities in Magneto-Hydrodynamics

A. Yu. Chebotarev, A. S. Savenkova

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (521 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm3761
Abstract: We study subdifferential initial boundary-value problems for the magneto-hydrodynamics (MHD) equations of a viscous incompressible liquid. We construct the solvability theory for an abstract evolution inequality in Hilbert space for operators with quadratic nonlinearity. The results obtained are applied to the study of MHD flows. For three-dimensional flows, we prove the existence of weak solutions of variational inequalities “globally” with respect to time, while, for two-dimensional flows, we establish the existence and uniqueness of strong solutions.
Keywords: viscous incompressible liquid, magneto-hydrodynamics equation, subdifferential initial boundary-value problem, variational inequality.
Received: 13.12.2005
English version:
Mathematical Notes, 2007, Volume 82, Issue 1, Pages 119–130
DOI: https://doi.org/10.1134/S0001434607070152
Bibliographic databases:
UDC: 517.95
Language: Russian
Citation: A. Yu. Chebotarev, A. S. Savenkova, “Variational Inequalities in Magneto-Hydrodynamics”, Mat. Zametki, 82:1 (2007), 135–149; Math. Notes, 82:1 (2007), 119–130
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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