Global well‐posedness of the Cauchy problem for certain magnetohydrodynamic‐α models |
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| Authors: | Yi Du Hua Qiu Zhengan‐Yao |
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| Affiliation: | 1. School of Mathematical Sciences, South China Normal University, Guangzhou 510631, People's Republic of China;2. School of Mathematics and Computational Science, Sun Yat‐Sen University, South China Agricultural University, Guangzhou, People's Republic of China;3. School of Mathematics and Computational Science, Sun Yat‐Sen University, Guangzhou, People's Republic of China |
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| Abstract: | 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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| Keywords: | magnetohydrodynamic Littlewood– Paley decomposition global well‐posedness |
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