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Mat. Zametki, 2007, Volume 82, Issue 1, Pages 135–149 (Mi mz3761)  

This article is cited in 4 scientific papers (total in 4 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

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

DOI: https://doi.org/10.4213/mzm3761

Full text: PDF file (521 kB)
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English version:
Mathematical Notes, 2007, 82:1, 119–130

Bibliographic databases:

UDC: 517.95
Received: 13.12.2005

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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  • https://doi.org/10.4213/mzm3761
  • http://mi.mathnet.ru/eng/mz/v82/i1/p135

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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. A. Yu. Chebotarev, A. A. Illarionov, E. V. Amosova, “Variatsionnye neravenstva, kraevye zadachi i optimalnoe upravlenie dlya sistemy Nave–Stoksa”, Dalnevost. matem. zhurn., 8:1 (2008), 121–140  mathnet  elib
    2. A. Yu. Chebotarev, “Control of magnetohydrodynamic flow in the formation of a magnetic field with a prescribed configuration”, Comput. Math. Math. Phys., 49:11 (2009), 1913–1920  mathnet  crossref  isi
    3. A. Yu. Chebotarev, “Stabilizatsiya neustoichivykh ravnovesnykh konfiguratsii v magnitnoi gidrodinamike”, Zh. vychisl. matem. i matem. fiz., 52:2 (2012), 312–318  mathnet  mathscinet  zmath
    4. A. Yu. Chebotarev, “Stabilization of equilibrium MHD configurations by external currents”, Comput. Math. Math. Phys., 52:12 (2012), 1670–1678  mathnet  crossref  mathscinet  zmath  isi  elib  elib
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