Geodesic
On an initial boundary-value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 167-184

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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 $W^{2,1}_p$ with $p>5/2$. The proof relies on the theory of general parabolic initial boundary-value problems. Bibliography: 16 titles. 
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     title = {On an initial boundary-value problem for the equation of magnetohydrodynamics with the {Hall} and ion-slip effects},
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G. Mulone; V. A. Solonnikov. On an initial boundary-value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Tome 221 (1995), pp. 167-184. http://geodesic.mathdoc.fr/item/ZNSL_1995_221_a10/