Abstract
This paper is concerned with the three-dimensional initial boundary-value problem for the equations of magnetohydrodynamics with additional nonlinear terms stemming from a more general relationship between the electric field and the current density. The problem governs the motion of a viscous incompressible conducting liquid in a bounded container with an ideal conducting surface. The existence of a solution which is close to a certain basic solution is proved. The solution is found in the anosotropic Sobolev spaces W 2,1p with p>5/2. The proof relies on the theory of general parabolic initial boundary-value problems. Bibliography: 16 titles.
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Dedicated to N. N. Uraltseva on her jubilee
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 221, 1995, pp. 167–184.
Translated by V. A. Solonnikov.
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Mulone, G., Solonnikov, V.A. On an initial boundary-value problem for the equation of magnetohydrodynamics with the hall and ion-slip effects. J Math Sci 87, 3381–3392 (1997). https://doi.org/10.1007/BF02355589
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DOI: https://doi.org/10.1007/BF02355589