| On the Blow-up Criterion of Smooth Solutions to the MHD System in BMO Space |
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| 作者姓名： | Bao-quan Yuan |
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| 作者单位： | [1]Academy of Mathematics ＆ Systems Science, Chinese Academy of Sciences, Beijing 100080, China [2]College of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454000, China |
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| 基金项目： | Supported by the National Natural Science Foundation of China （No.10571016） and Science Foundation for the Excellent Young Teacher of Henan Province. |
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| 摘 要： | In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO space. Let （u（x,t）,b（x,t）） be smooth solutions in （0, T）. It is shown that the solution （u（x, t）, b（x, t）） can be extended beyond t = T if （u（x,t）, b（x, t）） ∈ L^1 （0, T; BMO） or the vorticity （rot u（x, t）, rot b（x, t）） ∈ L^1 （0, T; BMO） or the deformation （Def u（x, t）, Def b（x, t）） ∈ L^1 （0, T; BMO）.
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| 关 键 词： | 磁发电机动态系统 BMO空间 平滑解 数学分析 |
| 收稿时间： | 2004-09-15 |
| 修稿时间： | 2004-09-152006-02-24 |
On the Blow-up Criterion of Smooth Solutions to the MHD System in BMO Space |
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| Bao-quan Yuan.On the Blow-up Criterion of Smooth Solutions to the MHD System in BMO Space[J].Acta Mathematicae Applicatae Sinica,2006,22(3):413-418. |
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| Authors: | Bao-quan Yuan |
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| Institution: | (1) Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing, 100080;(2) China College of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454000, China |
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| Abstract: | Abstract
In this paper we study the blow-up criterion of smooth solutions to the incompressible magnetohydrodynamics system in BMO
space. Let (u(x, t), b(x, t)) be smooth solutions in (0, T). It is shown that the solution (u(x, t), b(x, t)) can be extended beyond t = T if (u(x, t), b(x, t)) ∈ L
1(0, T; BMO) or the vorticity (rot u(x, t), rot b(x, t)) ∈ L1(0, T;BMO) or the deformation (Def u(x, t), Def b(x, t)) ∈ L1(0, T;BMO).
Supported by the National Natural Science Foundation of China (No.10571016) and Science Foundation for the Excellent Young
Teacher of Henan Province. |
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| Keywords: | Magneto-hydrodynamics system BMO space blow-up criterion |
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