Abstract
The well-posedness of the equations of fluid mechanics in the hydrostatic limit is well known to be a difficult problem. Partial results, both positive and negative, will be reviewed below. In this paper, it is shown that, for ideal magnetohydrodynamics, a magnetic field parallel to the flow direction can ensure well-posedness. The only condition required is that the flow is subalfvenic. The result has some relevance to viscoelastic flows of the upper convected Maxwell fluid, which, in the infinite Weissenberg number limit, is related to ideal MHD.
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Communicated by G.P. Galdi
This research was supported by the National Science Foundation under Grant DMS-1008426.
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Renardy, M. Well-Posedness of the Hydrostatic MHD Equations. J. Math. Fluid Mech. 14, 355–361 (2012). https://doi.org/10.1007/s00021-011-0073-y
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DOI: https://doi.org/10.1007/s00021-011-0073-y