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Mixed Boundary Value Problems for Stationary Magnetohydrodynamic Equations of a Viscous Heat-Conducting Fluid

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Abstract

We consider the boundary value problem for stationary magnetohydrodynamic equations of electrically and heat conducting fluid under inhomogeneous mixed boundary conditions for electromagnetic field and temperature and Dirichlet condition for the velocity. The problem describes the thermoelectromagnetic flow of a viscous fluid in 3D bounded domain with the boundary consisting of several parts with different thermo- and electrophysical properties. The global solvability of the boundary value problem is proved and the apriori estimates of the solution are derived. The sufficient conditions on the data are established which provide a local uniqueness of the solution.

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Authors and Affiliations

  1. Far Eastern Federal University, 8, Sukhanova St., Vladivostok, 690950, Russia

    Gennady Alekseev

  2. Institute of Applied Mathematics FEB RAS, 7, Radio St., Vladivostok, 690041, Russia

    Gennady Alekseev

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  1. Gennady Alekseev
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Correspondence to Gennady Alekseev.

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Communicated by O. Pironneau

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Alekseev, G. Mixed Boundary Value Problems for Stationary Magnetohydrodynamic Equations of a Viscous Heat-Conducting Fluid. J. Math. Fluid Mech. 18, 591–607 (2016). https://doi.org/10.1007/s00021-016-0253-x

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