Geodesic
Free boundary problem of magnetohydrodynamics
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 149-178

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We consider a free boundary problem governing the motion of a finite isolated mass of a viscous incompressible electrically conducting fluid in vacuum. Media is moving under the action of magnetic field and volume forces. We prove solvability of this free boundary problem in an infinite time interval under the additional smallness assumptions imposed on initial data and the external forces. 
@article{ZNSL_2014_425_a9,
     author = {E. V. Frolova},
     title = {Free boundary problem of magnetohydrodynamics},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {149--178},
     publisher = {mathdoc},
     volume = {425},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a9/}
}
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E. V. Frolova. Free boundary problem of magnetohydrodynamics. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 44, Tome 425 (2014), pp. 149-178. http://geodesic.mathdoc.fr/item/ZNSL_2014_425_a9/