| 摘要: |
| 借助分数阶拉普拉斯算子，考虑仅带有速度耗散项的广义三维MHD方程的整体正则性，运用Galerkin逼近、紧性理论和能量方法，给出了相关定理的修正证明.证明了当α ≥ 5/2时，方程存在唯一的强解. |
| 关键词: 广义magnetohydrodynamic(MHD) 整体正则性 整体存在性 速度耗散 |
| DOI：10.3969/J.ISSN.1000-5137.2019.03.009 |
| 分类号:O29 |
| 基金项目: |
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| Global regularity of the 3D generalized MHD equations with only velocity dissipation |
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CAI Xiaojing1, LIU Bingyu2
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1.School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China;2.School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
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| Abstract: |
| In this paper, we consider the global regularity of the three-dimensinal (3D) generalized magnetohydrodynamic (MHD) equations with only velocity dissipation in terms of fractional Laplacians. By the Galerkin approximation methods, the compactness and the energy method, we give a refined proof of the correlation theorem and prove the global existence and uniqueness of the strong solutions for any α ≥ 5/2. |
| Key words: generalized magnetohydrodynamic global regularity global existence velocity dissipation |
