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Keywords:
electrically conducting; bounded three dimensional domain; boundary perfectly conducting; displacement current; Maxwell’s equations; small periodic force; small positive epsilon; locally unique periodic solution
electrically conducting; bounded three dimensional domain; boundary perfectly conducting; displacement current; Maxwell’s equations; small periodic force; small positive epsilon; locally unique periodic solution
Summary:
This paper deals with a system of equations describing the motion of viscous electrically conducting incompressible fluid in a bounded three dimensional domain whose boundary is perfectly conducting. The displacement current appearing in Maxwell's equations, $\epsilon E_t$ is not neglected. It is proved that for a small periodic force and small positive #\epsilon# there exists a locally unique periodic solution of the investigated system. For $\epsilon \rightarrow 0$, these solutions are shown to convergeto a solution of the simplified (and usually considered) system of equations of magnetohydrodynamics.
References:
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