Control of Magnetohydrodynamic Flow in the Formationof a Magnetic Field with a Prescribed Configuration

摘要

Control problems for the viscous incompressible magnetohydrodynamic equations areconsidered. The goal is to produce a magnetic field with a prescribed structure at a given time by apply-ing 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 solv-ability conditions for the control problems are found.