Geodesic
The solvability of the initial boundary-value problem for magnetohydrodynamics
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 10, Tome 69 (1977), pp. 219-239

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The three-dimensional, nonlinear, time-dependent problem of magnetohydrodynamics is considered in the case where displacement currents cannot be neglected. The local unique solvability of the initial boundary-value problem for this system of equations is proved. 
@article{ZNSL_1977_69_a15,
     author = {L. Stupyalis},
     title = {The solvability of the initial boundary-value problem for magnetohydrodynamics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {219--239},
     publisher = {mathdoc},
     volume = {69},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_69_a15/}
}
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L. Stupyalis. The solvability of the initial boundary-value problem for magnetohydrodynamics. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 10, Tome 69 (1977), pp. 219-239. http://geodesic.mathdoc.fr/item/ZNSL_1977_69_a15/