Existence and Approximation of Statistical Solutions of the 3D MHD Equations  

作　　者：ZHANG Yuanyuan CHEN Guanggan 

机构地区：[1]School of Mathematics and Physics,Southwest University of Science and Technology,Mianyang 621010,China [2]School of Mathematical Sciences,and V.C.&V.R.Key Lab of Sichuan Province,Sichuan Normal University,Chengdu 610068,China

出　　处：《Journal of Partial Differential Equations》2024年第3期326-354,共29页偏微分方程（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12171343);the Sichuan Science and Technology Program(Grant No.2022JDTD0019).

摘　　要：This paper focuses on the statistical characteristics of the 3D MHD equations.We firstly establish an existence theorem of a Vishik-Fursikov measure of the 3D MHD equations by taking advantage of the Krein-Milman theorem along with some functional and measure theories.Then by applying the Topsoe lemma on the constructed trajectory space possessing some special topological properties,we show that the Vishik-Fursikov measure and the stationary Vishik-Fursikov statistical solution of the 3D MHD system are approximated by the counterparts of the 3D MHD-αsystem,respectively,as the parameterαdecreases to zero.

关 键 词：3D MHD equations Vishik-Fursikov measures stationary statistical solutions convergence of measures 

分 类 号：O175.29[理学—数学]