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Bull. Korean Math. Soc. 2010; 47(2): 231-249
Printed March 1, 2010
https://doi.org/10.4134/BKMS.2010.47.2.231
Copyright © The Korean Mathematical Society.
Asymptotic study of mixed rotating MHD system
Ridha Selmi
Facult\'e des Sciences de Gab\`es
Asymptotic behavior of three-dimensional mixed, periodic and rotating magnetohydrodynamic system is investigated as the Rossby number goes to zero. The system presents the difficulty to be singular and mixed, that is hyperbolic in the vertical direction and parabolic in the horizontal one. The divergence free condition and the spectral properties of the penalization operator are crucial in the proofs. The main tools are the energy method, the Schochet's method and products laws in anisotropic Sobolev spaces.
Keywords: MHD system, hyperbolic-parabolic system, anisotropic Sobolev spaces, divergence free condition, asymptotic behavior, Schocht's methods
MSC numbers: 35B10, 35B25, 35B40
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