×
Rappaz, J.; Touzani, R.

On a two-dimensional magnetohydrodynamic problem. I: Modelling and analysis. (English) Zbl 0738.76086

RAIRO, Modélisation Math. Anal. Numér. 26, No. 2, 347-364 (1992).
Summary: We consider a two-dimensional magnetohydrodynamic system of equations describing the motion of a conducting fluid in which eddy currents flow. The mathematical model is derived and existence of solutions is proved by using fixed point techniques. Uniqueness is obtained under restrictive conditions on the involved physical parameters.

Cited in 1 Review
Cited in 4 Documents

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
35Q60 PDEs in connection with optics and electromagnetic theory

Keywords:

two-dimensional magnetohydrodynamic system; conducting fluid; existence of solutions; fixed point techniques; uniqueness
PDF BibTeX XML Cite
\textit{J. Rappaz} and \textit{R. Touzani}, RAIRO, Modélisation Math. Anal. Numér. 26, No. 2, 347--364 (1992; Zbl 0738.76086)
Full Text: DOI EuDML

References:

[1] O. BESSON, J. BOURGEOIS, P. A. CHEVALIER, J. RAPPAZ, R. TOUZANI, Numerical modelling of electromagnetic casting processes, J. Comput. Phys., Vol. 92, No. 2 (1991) 482-507. Zbl0721.65076 MR1094260 · Zbl 0721.65076
[2] J. BOURGEOIS, P. A. CHEVALIER, M. PICASSO, J. RAPPAZ, R. TOUZANI, An MHD problem in the Aluminium industry, Proceedings of the 7th International Conference on Finite Elements in Flow Problems, Huntsville, Alabama (1989).
[3] M. CROUZEIX, J. DESCLOUX, A bidimensional electromagnetic problem, SIAM J. Math. Anal., 21, No. 3 (1990), pp. 577-592. Zbl0709.35029 MR1046790 · Zbl 0709.35029
[4] L. LANDAU, E. LIFCHITZ, Electrodynamics of continuous media, Pergamon Press, London, 1960. Zbl0122.45002 · Zbl 0122.45002
[5] J.-C. NEDELEC, Approximation des équations intégrales en mécanique et en physique, Rapport du Centre de Mathématiques Appliquées, Ecole Polytechnique, Palaiseau (1977).
[6] [6] J. LERAY, J. SCHAUDER, Topologie et équations fonctionnelles, Ann. Sci. Ecole Norm. Sup., 51 (1934), pp. 45-78. MR1509338 JFM60.0322.02 · JFM 60.0322.02
[7] P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, Monographs and Studies in Mathematics 24, 1985. Zbl0695.35060 MR775683 · Zbl 0695.35060
[8] R. TEMAM, Navier-Stokes Equations, North-Holland, Amsterdam, 1984. Zbl0568.35002 MR769654 · Zbl 0568.35002
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.