# Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem

Aplikace matematiky (1983)

- Volume: 28, Issue: 5, page 344-356
- ISSN: 0862-7940

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topŠtědrý, Milan, and Vejvoda, Otto. "Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem." Aplikace matematiky 28.5 (1983): 344-356. <http://eudml.org/doc/15314>.

@article{Štědrý1983,

abstract = {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 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.},

author = {Štědrý, Milan, Vejvoda, Otto},

journal = {Aplikace matematiky},

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},

language = {eng},

number = {5},

pages = {344-356},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem},

url = {http://eudml.org/doc/15314},

volume = {28},

year = {1983},

}

TY - JOUR

AU - Štědrý, Milan

AU - Vejvoda, Otto

TI - Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem

JO - Aplikace matematiky

PY - 1983

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 28

IS - 5

SP - 344

EP - 356

AB - 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 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.

LA - eng

KW - 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

UR - http://eudml.org/doc/15314

ER -

## References

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- O. A. Ladyženskaja V. A. Solonnikov, Solutions of some non-stationary problems of.magnetohydrodynamics for incompressible fluid, (Russian.) Trudy Mat. Inst. V. A. Steklova, 59 (1960), 115-173. (1960) MR0170130
- O. A. Ladyženskaja V. A. Solonnikov, On the principle of linearization and invariant manifolds in problems of magnetohydrodynamics, (Russian.) Zapiski naučnych seminarov LOMI, 38 (1973), 46-93. (1973) MR0377310
- O. A. Ladyženskaja, Mathematical Problems of the Dynamics of Viscous Incompressible Liquid, (Russian.) Nauka, Moskva, 1970. (1970) MR0271559
- A. Milani, On a singular perturbation problem for the linear Maxwell equations, Quaderni di Matematica, Università di Torino, n° 20, 1980, 11-16. (1980) Zbl0478.35010
- A. Milani, On a singular perturbation problem for the Maxwell equations in a multiply connected domain, Rend. Sem. Mat. Univers. Politecn. Torino, 38, 1 (1980), 123-132. (1980) Zbl0464.35006MR0608934
- J. A. Shercliff, A Textbook of Magnetohydrodynamics, Pergamon, Oxford 1965. (1965) MR0185961
- L. Stupjalis, A nonstationary problem of magnetohydrodynamics, (Russian.) Zapiski naučnych seminarov LOMI, 52 (1975), 175-217. (1975) MR0464896
- L. Stupjalis, On solvability of an initial-boundary value problem of magnetohydrodynamics, (Russian.) Zapiski naučnych seminarov LOMÍ, 69 (1977), 219-239. (1977) MR0499834
- L. Stupjalis, A nonstationary problem of magnetohydrodynamics in the case of two spatial variables, (Russian.) Trudy Mat. Inst. V. A. Steklova, 147 (1980), 156-168. (1980) MR0573906

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