Well-posedness and exponential mixing for stochastic magneto-hydrodynamic equations with fractional dissipations  

作　　者：Wei HONG Shihu LI Wei LIU 

机构地区：[1]School of Mathematics and Statistics,Jiangsu Normal University,Xuzhou 221116,China [2]Center for Applied Mathematics,Tianjin University,Tianjin 300072,China [3]RIMS,Jiangsu Normal University,Xuzhou 221116,China

出　　处：《Frontiers of Mathematics in China》2021年第2期425-457,共33页中国高等学校学术文摘·数学（英文）

基　　金：The research of S.Li was supported by the National Natural Science Foundation of China(Grant No.12001247);the Natural Science Foundation of Jiangsu Province(No.BK20201019);the Natural Science Foundation of Jiangsu Higher Education Institutions of China(No.20KJB110015);the Foundation of Jiangsu Normal University(No.19XSRX023);The research of W.Liu was supported by the National Natural Science Foundation of China(Grant Nos.11822106,11831014,12090011)and the PAPD of Jiangsu Higher Education Institutions.

摘　　要：Consider d-dimensional magneto-hydrodynamic(MHD)equations with fractional dissipations driven by multiplicative noise.First,we prove the existence of martingale solutions for stochastic fractional MHD equations in the case of d=2,3 andα∧β〉0,whereα,βare the parameters of the fractional dissipations in the equation.Second,for d=2,3 andα∧β≥12+d4,we show the pathwise uniqueness of solutions and then obtain the existence and uniqueness of strong solutions using the Yamada-Watanabe theorem.Furthermore,we establish the exponential mixing property for stochastic MHD equations with degenerate multiplicative noise when d=2,3 andα∧β≥12+d4.

关 键 词：Magneto-hydrodynamic(MHD)equation martingale solution degenerate noise ERGODICITY exponential mixing 

分 类 号：O17[理学—数学]