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Global well‐posedness of the Cauchy problem for certain magnetohydrodynamic‐α models
Author(s) -
Du Yi,
Qiu Hua
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1265
Subject(s) - magnetohydrodynamics , sobolev space , magnetohydrodynamic drive , initial value problem , mathematics , cauchy problem , space (punctuation) , mathematical analysis , compressibility , physics , computer science , magnetic field , mechanics , quantum mechanics , operating system
This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics‐α model. In the Sobolev space with fractional index s >1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as α→0, the MHD‐α model reduces to the MHD equations, and the solutions of the MHD‐α model converge to a pair of solutions for the MHD equations. Copyright © 2010 John Wiley & Sons, Ltd.
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