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Equations of magnetohydrodynamics of compressible fluid: Periodic solutions. (English) Zbl 0591.76184
(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

76W05 Magnetohydrodynamics and electrohydrodynamics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
Full Text: EuDML
[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 · numdam:ASNSP_1983_4_10_4_607_0 · eudml:83920
[7] N. G. Van Kampen B. U. Felderhof: Theoretical Methods in Plasma Physics. North-Holland Publishing Company - Amsterdam, 1967. · Zbl 0159.29601
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