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Zap. Nauchn. Sem. POMI, 1995, Volume 221, Pages 167–184 (Mi znsl4302)  

This article is cited in 3 scientific papers (total in 3 papers)

On an initial boundary-value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects

G. Mulonea, V. A. Solonnikovb

a Dipartimento di matematica, Universitá di Napoli, Italia
b St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: This paper is concerned with the three-dimensional initial boundary-value problem for the equations of magnetohydrodynamics with additional nonlinear terms stemming from a more general relationship between the electric field and the current density. The problem governs the motion of a viscous incompressible conducting liquid in a bounded container with an ideal conducting surface. The existence of a solution which is close to a certain basic solution is proved. The solution is found in the anosotropic Sobolev spaces $W^{2,1}_p$ with $p>5/2$. The proof relies on the theory of general parabolic initial boundary-value problems. Bibliography: 16 titles.

Full text: PDF file (619 kB)

English version:
Journal of Mathematical Sciences (New York), 1997, 87:2, 3381–3392

Bibliographic databases:

UDC: 517.9
Received: 01.12.1994

Citation: G. Mulone, V. A. Solonnikov, “On an initial boundary-value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects”, Boundary-value problems of mathematical physics and related problems of function theory. Part 26, Zap. Nauchn. Sem. POMI, 221, POMI, St. Petersburg, 1995, 167–184; J. Math. Sci. (New York), 87:2 (1997), 3381–3392

Citation in format AMSBIB
\Bibitem{MulSol95}
\by G.~Mulone, V.~A.~Solonnikov
\paper On an initial boundary-value problem for the equation of magnetohydrodynamics with the Hall and ion-slip effects
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 221
\pages 167--184
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4302}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1359755}
\zmath{https://zbmath.org/?q=an:0927.76100|0923.76353}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 2
\pages 3381--3392
\crossref{https://doi.org/10.1007/BF02355589}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Alekseev, R. V. Brizitskii, “Razreshimost smeshannoi zadachi dlya statsionarnykh uravnenii magnitnoi gidrodinamiki vyazkoi zhidkosti”, Dalnevost. matem. zhurn., 3:2 (2002), 285–301  mathnet
    2. Popa C., Sritharan S., “Fluid-Magnetic Splitting of the Magnetohydrodynamic Equations”, Math. Models Meth. Appl. Sci., 13:6 (2003), 893–917  crossref  zmath  isi
    3. G. V. Alekseev, “Zadachi upravleniya dlya statsionarnykh modelei magnitnoi gidrodinamiki vyazkoi neszhimaemoi zhidkosti”, Dalnevost. matem. zhurn., 6:1-2 (2005), 117–145  mathnet  elib
  • Записки научных семинаров ПОМИ
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