Equations of magnetohydrodynamics of compressible fluid: Periodic solutions

Milan Štědrý; Otto Vejvoda

Aplikace matematiky (1985)

  • Volume: 30, Issue: 2, page 77-91
  • ISSN: 0862-7940

Abstract

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The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.

How to cite

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Štědrý, Milan, and Vejvoda, Otto. "Equations of magnetohydrodynamics of compressible fluid: Periodic solutions." Aplikace matematiky 30.2 (1985): 77-91. <http://eudml.org/doc/15387>.

@article{Štědrý1985,
abstract = {The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.},
author = {Štědrý, Milan, Vejvoda, Otto},
journal = {Aplikace matematiky},
keywords = {periodic solutions; small initial velocity; global existence; exponential stability of solutions; external forces; displacement current; periodic solutions; small initial velocity; global existence; exponential stability of solutions; external forces; displacement current},
language = {eng},
number = {2},
pages = {77-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equations of magnetohydrodynamics of compressible fluid: Periodic solutions},
url = {http://eudml.org/doc/15387},
volume = {30},
year = {1985},
}

TY - JOUR
AU - Štědrý, Milan
AU - Vejvoda, Otto
TI - Equations of magnetohydrodynamics of compressible fluid: Periodic solutions
JO - Aplikace matematiky
PY - 1985
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 30
IS - 2
SP - 77
EP - 91
AB - The authors prove the global existence and exponential stability of solutions of the given system of equations under the condition that the initial velocities and the external forces are small and the initial density is not far from a constant one. If the external forces are periodic, then solutions periodic with the same period are obtained. The investigated system of equations is a bit non-standard - for example the displacement current in the Maxwell equations is not neglected.
LA - eng
KW - periodic solutions; small initial velocity; global existence; exponential stability of solutions; external forces; displacement current; periodic solutions; small initial velocity; global existence; exponential stability of solutions; external forces; displacement current
UR - http://eudml.org/doc/15387
ER -

References

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  1. E. B. Byhovskiĭ, A solution of a mixed problem for a system of Maxwell's equations in the case of ideally conducting boundary, (Russian). Vestnik Leningradskogo Univ. 1957, No. 13, 50-66. (1957) MR0098567
  2. 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
  3. J. A. Shercliff, A Textbook of Magnetohydrodynamics, Pergamon, Oxford 1965. (1965) MR0185961
  4. M. Štědrý O. Vejvoda, Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem, Aplikace matematiky 28 (1983), 344-356. (1983) MR0712911
  5. L. Stupjalis, On solvability of an initial-boundary value problem of magnetohydrodynamics, (Russian.) Zapiski naučnych seminarov LOMI, 69 (1977), 219 - 239. (1977) MR0499834
  6. A. Valli, Periodic and stationary solutions for compressible Navier-Stokes equations via a stability method, Annali Scuola Normale Superiore Pisa, 10 (1983), 607-647. (1983) Zbl0542.35062MR0753158
  7. N. G. Van Kampen B. U. Felderhof, Theoretical Methods in Plasma Physics, North-Holland Publishing Company - Amsterdam, 1967. (1967) 

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