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ArticleOriginal scientific text

Title

A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process

Authors 1

Affiliations

  1. Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland

Abstract

We investigate the behaviour of the meniscus of a drop of liquid aluminium in the neighbourhood of a state of equilibrium under the influence of weak electromagnetic forces. The mathematical model comprises both Maxwell and Navier-Stokes equations in 2D. The meniscus is governed by the Young-Laplace equation, the data being the jump of the normal stress. To show the existence and uniqueness of the solution we use the classical implicit function theorem. Moreover, the differentiability of the operator solving this problem is established.

Keywords

ENG
free boundary, local existence and uniqueness, implicit function theorem, steady plane magnetohydrodynamics, electromagnetic casting

Bibliography

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Annales Polonici Mathematici
1995/61/3
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Pages:
195-223
Main language of publication
English
Received
1993-03-03
Accepted
1993-05-30
Published
1995
Exact and natural sciences