Štědrý, Milan; Vejvoda, Otto Equations of magnetohydrodynamics of compressible fluid: Periodic solutions. (English) Zbl 0591.76184 Apl. Mat. 30, 77-91 (1985). (From authors’ summary.) 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. Reviewer: P.Smith Cited in 3 Documents MSC: 76W05 Magnetohydrodynamics and electrohydrodynamics 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:periodic solutions; small initial velocity; global existence; exponential stability of solutions; external forces; displacement current PDF BibTeX XML Cite \textit{M. Štědrý} and \textit{O. Vejvoda}, Apl. Mat. 30, 77--91 (1985; Zbl 0591.76184) Full Text: EuDML References: [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. [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. [3] J. A. Shercliff: A Textbook of Magnetohydrodynamics. Pergamon, Oxford 1965. [4] M. Štědrý O. Vejvoda: Small time-periodic solutions of equations of magnetohydrodynamics as a singularly perturbed problem. Aplikace matematiky 28 (1983), 344-356. [5] L. Stupjalis: On solvability of an initial-boundary value problem of magnetohydrodynamics. (Russian.) Zapiski naučnych seminarov LOMI, 69 (1977), 219 - 239. · Zbl 0363.76085 [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. · Zbl 0542.35062 [7] N. G. Van Kampen B. U. Felderhof: Theoretical Methods in Plasma Physics. North-Holland Publishing Company - Amsterdam, 1967. · Zbl 0159.29601 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.