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.
@article{bwmeta1.element.bwnjournal-article-apmv61z3p195bwm,
author = {Tomasz Roli\'nski},
title = {A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process},
journal = {Annales Polonici Mathematici},
volume = {62},
year = {1995},
pages = {195-223},
zbl = {0829.76095},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z3p195bwm}
}
Tomasz Roliński. A free boundary stationary magnetohydrodynamic problem in connection with the electromagnetic casting process. Annales Polonici Mathematici, Tome 62 (1995) pp. 195-223. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z3p195bwm/
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