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 
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/
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     title = {Control of magnetohydrodynamic flow in the formation of a~magnetic field with a~prescribed configuration},
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     pages = {2001--2009},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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