三维稳态磁流体动力学方程的Liouville定理  

On the Liouville Theorems for 3 D Stationary Magnetohydrodynamic Equations

作　　者：田琴 向长林 别群益[1,2] TIAN Qin;XIANG Changlin;BIE Qunyi(College of Science,China Three Gorges University,Yichang,Hubei 443002,P.R.China;Three Gorges Mathematical Research Center,China Three Gorges University,Yichang,Hubei 443002,P.R.China)

机构地区：[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

出　　处：《应用数学和力学》2023年第10期1250-1259,共10页Applied Mathematics and Mechanics

基　　金：国家自然科学基金项目(11871305;12271296)。

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.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.

关 键 词：磁流体动力学方程 LIOUVILLE定理 Caccioppoli型不等式 

分 类 号：O175.2[理学—数学]