| Title:
|
Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem (English) |
| Author:
|
Štědrý, Milan |
| Author:
|
Vejvoda, Otto |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
5 |
| Year:
|
1983 |
| Pages:
|
344-356 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
electrically conducting |
| Keyword:
|
bounded three dimensional domain |
| Keyword:
|
boundary perfectly conducting |
| Keyword:
|
displacement current |
| Keyword:
|
Maxwell’s equations |
| Keyword:
|
small periodic force |
| Keyword:
|
small positive epsilon |
| Keyword:
|
locally unique periodic solution |
| MSC:
|
35A07 |
| MSC:
|
35B10 |
| MSC:
|
35B25 |
| MSC:
|
76W05 |
| idZBL:
|
Zbl 0524.76101 |
| idMR:
|
MR0712911 |
| DOI:
|
10.21136/AM.1983.104046 |
| . |
| Date available:
|
2008-05-20T18:23:06Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104046 |
| . |
| Reference:
|
[1] N. G. Van Kampen B. U. Felderhof: Theoretical Methods in Plasma Physics.North-Holland Publishing Company - Amsterdam, 1967. |
| Reference:
|
[2] 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. MR 0170130 |
| Reference:
|
[3] 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. MR 0377310 |
| Reference:
|
[4] O. A. Ladyženskaja: Mathematical Problems of the Dynamics of Viscous Incompressible Liquid.(Russian.) Nauka, Moskva, 1970. MR 0271559 |
| Reference:
|
[5] A. Milani: On a singular perturbation problem for the linear Maxwell equations.Quaderni di Matematica, Università di Torino, n° 20, 1980, 11-16. Zbl 0478.35010 |
| Reference:
|
[6] 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. Zbl 0464.35006, MR 0608934 |
| Reference:
|
[7] J. A. Shercliff: A Textbook of Magnetohydrodynamics.Pergamon, Oxford 1965. MR 0185961 |
| Reference:
|
[8] L. Stupjalis: A nonstationary problem of magnetohydrodynamics.(Russian.) Zapiski naučnych seminarov LOMI, 52 (1975), 175-217. MR 0464896 |
| Reference:
|
[9] L. Stupjalis: On solvability of an initial-boundary value problem of magnetohydrodynamics.(Russian.) Zapiski naučnych seminarov LOMÍ, 69 (1977), 219-239. MR 0499834 |
| Reference:
|
[10] 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. MR 0573906 |
| . |
