| 磁流体方程组弱解在负指标Besov空间中基于旋度和电流的正则性标准 |
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| 引用本文： | 原保全.磁流体方程组弱解在负指标Besov空间中基于旋度和电流的正则性标准[J].数学进展,2008,37(4). |
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| 作者姓名： | 原保全 |
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| 基金项目： | 国家博士后科学基金，河南省自然科学基金，河南省教育厅科技攻关项目 |
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| 摘 要： | 本文研究了不可压磁流体方程组弱解的正则性准则,设(u(t,x),6(t,x))是不可压磁流体方程组在(O,T)上的光滑解,如果旋度和电流密度满足(▽× u,▽× b) ∈ L 2-a/2 (O, T;B-aa∞, ∞(R3)) ηL1-a/2(O,T;B-∞1,-a∞(R3)),0＜α＜1,则光滑解(u(t,x),b(t,x))可以连续延拓到(O,T'),T'＞T.而且这个条件可以保证满足能量不等式的弱解是(O,T)上的光滑解.
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| 关 键 词： | 磁流体方程组 弱解的正则性 负指标Besov空间 |
Regularity Criterion of Weak Solutions to the MHD System Based on Vorticity and Electric Current in Negative Index Besov Spaces |
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| YUAN Baoquan.Regularity Criterion of Weak Solutions to the MHD System Based on Vorticity and Electric Current in Negative Index Besov Spaces[J].Advances in Mathematics,2008,37(4). |
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| Authors: | YUAN Baoquan |
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| Abstract: | In this paper, the regularity criterion of weak solutions to the incompressible magneto-hydrodynamic equations is studied. Let (u(t, x), b(t, x)) be smooth solutions in (O, T), it is shown that the solution (u, b) can be extended beyond T provided that the vorticity and electric current (▽× u,▽× b) ∈ L 2/2-a (O, T;B-aa∞, ∞(R3)) ηL2/1-a(O,T;B-∞1,-a∞(R3)),0＜α＜1.Moreover this condition ensures that the solution is a smooth solution if it satisfies the energy inequality. |
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| Keywords: | Magneto-hydrodynamical system regularity of weak solutions negative index Besov spaces |
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