Ergodicity of stochastic Magneto-Hydrodynamic equations driven by α-stable noise

被引：11

作者：

Shen, Tianlong ^{[1
]}

Huang, Shanhua ^{[1
]}

机构：

[1] Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 446卷 / 01期

关键词：

Stochastic Magneto-Hydrodynamic equation; Ergodicity; alpha-Stable noises; Invariant measure; NAVIER-STOKES EQUATIONS; VISCOUS MHD EQUATIONS; EXPONENTIAL ERGODICITY; REGULARITY CRITERIA; WEAK SOLUTIONS; FLOWS DRIVEN; LEVY NOISE; EXISTENCE; SPDES;

D O I：

10.1016/j.jmaa.2016.08.050

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The current paper is devoted to the ergodicity of stochastic Magneto-Hydrodynamic equations driven by alpha-stable noise with alpha is an element of (3/2, 2). By the maximal inequality for the stochastic alpha-stable convolution and vorticity transformation, the well-posedness of the mild solution for stochastic Magneto-Hydrodynamic equation is established. Due to the discontinuous trajectories, the existence and uniqueness of the invariant measure for stochastic Magneto-Hydrodynamic equation are obtained by the strong Feller property and the accessibility to zero instead of the irreducibility. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：746 / 769

页数：24

共 36 条

[1] Parabolic SPDEs driven by Poisson white noise [J].

Albeverio, S ;

Wu, JL ;

Zhang, TS .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1998, 74 (01) :21-36

[2]

[Anonymous], 2007, ENCY MATH ITS APPL

[3]

[Anonymous], 2011, J DIFFERENTIAL EQUAT

[4]

Applebaum D., 2004, CAMBRIDGE STUD ADV M

[5] Existence and ergodicity for the two-dimensional stochastic magneto-hydrodynamics equations [J].

Barbu, Viorel ;

Da Prato, Giuseppe .

APPLIED MATHEMATICS AND OPTIMIZATION, 2007, 56 (02) :145-168

[6]

CABANNES H., 1970, Theoretical Magnetofluiddynamics

[7] Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion [J].

Cao, Chongsheng ;

Wu, Jiahong .

ADVANCES IN MATHEMATICS, 2011, 226 (02) :1803-1822

[8]

Cowling T. G., 1976, THEORETICAL MAGNETOH

[9] Exponential Ergodicity of Stochastic Burgers Equations Driven by α-Stable Processes [J].

Dong, Zhao ;

Xu, Lihu ;

Zhang, Xicheng .

JOURNAL OF STATISTICAL PHYSICS, 2014, 154 (04) :929-949

[10] INVARIANT MEASURES OF STOCHASTIC 2D NAVIER-STOKES EQUATIONS DRIVEN BY α-STABLE PROCESSES [J].

Dong, Zhao ;

Xu, Lihu ;

Zhang, Xicheng .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2011, 16 :678-688

← 1 2 3 4 →