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Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem
Applications of Mathematics, Tome 28 (1983) no. 5, pp. 344-356
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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.
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.
DOI : 10.21136/AM.1983.104046
Classification : 35A07, 35B10, 35B25, 76W05
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 
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Štědrý, Milan; Vejvoda, Otto. Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem. Applications of Mathematics, Tome 28 (1983) no. 5, pp. 344-356. doi: 10.21136/AM.1983.104046

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