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 TMF, 1992, Volume 92, Number 2, Pages 269–292 (Mi tmf1503)

Rapidly oscillating asymptotic solution of magnetohydrodynamic equations in the Tokamak approximation

V. P. Maslov, G. A. Omel'yanov

Moscow Institute of Electronic Engineering

Abstract: An asymptotic solution of the magnetohydrodynamic equations for large Reynolds numbers is constructed in the approximation of a strong longitudinal magnetic field. Model equations that generalize the Kadomtsev–Pogutze equations to the case of toroidal symmetry are derived. The asymptotic stability of the constructed solution is demonstrated.

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English version:
Theoretical and Mathematical Physics, 1992, 92:2, 879–895

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Citation: V. P. Maslov, G. A. Omel'yanov, “Rapidly oscillating asymptotic solution of magnetohydrodynamic equations in the Tokamak approximation”, TMF, 92:2 (1992), 269–292; Theoret. and Math. Phys., 92:2 (1992), 879–895

Citation in format AMSBIB
\Bibitem{MasOme92} \by V.~P.~Maslov, G.~A.~Omel'yanov \paper Rapidly oscillating asymptotic solution of magnetohydrodynamic equations in the Tokamak approximation \jour TMF \yr 1992 \vol 92 \issue 2 \pages 269--292 \mathnet{http://mi.mathnet.ru/tmf1503} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1226015} \zmath{https://zbmath.org/?q=an:0786.76102} \transl \jour Theoret. and Math. Phys. \yr 1992 \vol 92 \issue 2 \pages 879--895 \crossref{https://doi.org/10.1007/BF01015555} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992LB54300007} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. A. Omel'yanov, “Existence of a solution to the equations of magnetohydrodynamics with helical symmetry in the tokamak approximation”, Math. Notes, 53:6 (1993), 611–621
2. V. P. Maslov, G. A. Omel'yanov, “Three-scale expansion of the solution of the magnetohydrodynamic equations and the Reynolds equation for a tokamak”, Theoret. and Math. Phys., 98:2 (1994), 202–211
3. A. I. Shafarevich, “The Navier–Stokes equations: Asymptotic solutions describing tangential discontinuities”, Math. Notes, 67:6 (2000), 792–801
4. Maslov, VP, “Rapidly oscillating asymptotic solutions of the Navier–Stokes equations, coherent structures, Fomenko invariants, Kolmogorov spectrum, and flicker noise”, Russian Journal of Mathematical Physics, 13:4 (2006), 414
5. V. P. Maslov, A. I. Shafarevich, “Asymptotic solutions of Navier–Stokes equations and topological invariants of vector fields and Liouville foliations”, Theoret. and Math. Phys., 180:2 (2014), 967–982
6. V. P. Maslov, A. I. Shafarevich, “Fomenko invariants in the asymptotic theory of the Navier–Stokes equations”, J. Math. Sci., 225:4 (2017), 666–680
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