A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows

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Original languageEnglish
Pages (from-to)805-847
Journal / PublicationArchive for Rational Mechanics and Analysis
Issue number3
Publication statusPublished - Jun 2014
Externally publishedYes


In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions n = 2 and 3 by adopting a geometrical point of view used in Christodoulou and Lindblad (Commun Pure Appl Math 53:1536-1602, 2000), and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids. © 2014 Springer-Verlag Berlin Heidelberg.