Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Variational approach to nonlinear gravity-driven instabilities in a MHD setting

Author: Hyung Ju Hwang
Journal: Quart. Appl. Math. 66 (2008), 303-324
MSC (2000): Primary 76E30
Published electronically: February 8, 2008
MathSciNet review: 2416775
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Abstract: We establish a variational framework for nonlinear instabilities in a setting of the ideal magnetohydrodynamic (MHD) equations. We apply a variational method to unstable smooth steady states for both incompressible and compressible ideal MHD equations. The destabilizing effect of compressibility is justified along with the stabilizing effect of magnetic field lines arising in the MHD dynamics. This generalizes the result of the Rayleigh-Taylor instability for incompressible fluids in the absence of magnetic field lines; see Hwang and Guo, On the dynamical Rayleigh-Taylor instability, Arch. Rational Mech. Anal. 167 (2003), 235-253.

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Additional Information

Hyung Ju Hwang
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea
Email: hjhwang@postech.ac.kr

DOI: https://doi.org/10.1090/S0033-569X-08-01116-1
Received by editor(s): July 1, 2006
Published electronically: February 8, 2008
Article copyright: © Copyright 2008 Brown University

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