Geodesic
Control of magnetohydrodynamic flow in the formation of a magnetic field with a prescribed configuration
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2001-2009

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Control problems for the viscous incompressible magnetohydrodynamic equations are considered. The goal is to produce a magnetic field with a prescribed structure at a given time by applying electromotive forces so as to minimize Joule heating or the work done on the conduction currents. Based on estimates obtained for the solution of a subdifferential Cauchy problem for the Navier–Stokes-type equations, the possibility of producing the required magnetic field is proved and the solvability conditions for the control problems are found. 
@article{ZVMMF_2009_49_11_a7,
     author = {A. Yu. Chebotarev},
     title = {Control of magnetohydrodynamic flow in the formation of a~magnetic field with a~prescribed configuration},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2001--2009},
     publisher = {mathdoc},
     volume = {49},
     number = {11},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a7/}
}
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A. Yu. Chebotarev. Control of magnetohydrodynamic flow in the formation of a magnetic field with a prescribed configuration. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2001-2009. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a7/