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Variational inequalities in magneto-hydrodynamics

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Abstract

We study subdifferential initial boundary-value problems for the magneto-hydrodynamics (MHD) equations of a viscous incompressible liquid. We construct a 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.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Far-Eastern Division, Russian Academy of Sciences, Vladivostok

    A. Yu. Chebotarev & A. S. Savenkova

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  1. A. Yu. Chebotarev
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  2. A. S. Savenkova
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Correspondence to A. Yu. Chebotarev.

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Chebotarev, A.Y., Savenkova, A.S. Variational inequalities in magneto-hydrodynamics. Math Notes 82, 119–130 (2007). https://doi.org/10.1134/S0001434607070152

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  • DOI: https://doi.org/10.1134/S0001434607070152

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