三维稳态磁流体动力学方程的Liouville定理

田琴; 向长林; 别群益

doi:10.21656/1000-0887.430375

三维稳态磁流体动力学方程的Liouville定理

doi: 10.21656/1000-0887.430375

田琴^{1, 2,},
向长林^{1, 2, ,},
别群益^{1, 2,}

1.
三峡大学理学院，湖北宜昌 443002
2.
三峡大学三峡数学研究中心，湖北宜昌 443002

基金项目:

国家自然科学基金项目 11871305

国家自然科学基金项目 12271296

详细信息

作者简介:
田琴(1998—)，女，硕士生(E-mail: 1321540194@qq.com)

别群益(1970—)，男，教授，博士，博士生导师(E-mail: qybie@126.com)

通讯作者:
向长林(1984—)，男，副教授，博士，博士生导师(通讯作者. E-mail: changlin.xiang@ctgu.edu.cn)

中图分类号: O175.2
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- 被引次数: 0
出版历程
- 收稿日期: 2022-11-22
- 修回日期: 2023-03-04
- 刊出日期: 2023-10-31

On the Liouville Theorems for 3D Stationary Magnetohydrodynamic Equations

TIAN Qin^{1, 2
,},
XIANG Changlin^{1, 2
, ,},
BIE Qunyi^{1, 2
,}

1.
College of Science, China Three Gorges University, Yichang, Hubei 443002, P.R. China
2.
Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P.R. China

摘要

摘要: 研究了三维稳态磁流体动力学方程的Liouville定理. 首先由能量估计建立了一个Caccioppoli型不等式，再结合Sobolev嵌入得到了Liouville定理成立的3个充分条件，其中一个充分条件表明：若三维稳态磁流体动力学方程的光滑解( u , b )∈L^p，3/2 < p < 3，则 u = b ≡ 0 . 该结果在不需要有限Dirichlet积分的条件下，将Lebesgue空间中可积指标的下界从2扩展至3/2，改进和推广了已有关于磁流体动力学方程Liouville定理的一些结论.
- 磁流体动力学方程 /
- Liouville定理 /
- Caccioppoli型不等式
Abstract: The Liouville theorems for 3D stationary magnetohydrodynamic equations were studied. First, a Caccioppoli type inequality was obtained with the energy method, then 3 sufficient conditions for the Liouville theorems were obtained based on the Sobolev embedding theorems, of which 1 sufficient condition indicates that, given a smooth solution to the 3D stationary magnetohydrodynamic equation satisfying( u , b )∈L^p, 3/2 < p < 3, equality u = b ≡ 0 will be tenable. This work extends the lower bound of the integrable index in the Lebesgue space from 2 to 3/2 without the finite Dirichlet integral condition, which improves and generalizes some conclusions about the Liouville theorems for stationary magnetohydrodynamic equations.
- magnetohydrodynamic equations /
- Liouville theorems /
- Caccioppoli type inequality

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参考文献(17)

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