Liouville-type theorems for the stationary incompressible inhomogeneous Hall-MHD and MHD equations

被引：3

作者：

Liu, Pan ^{[1
,2
]}

机构：

[1] Yulin Univ, Sch Math & Stat, Yulin 719000, Shaanxi, Peoples R China

[2] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2023年 / 17卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Liouville-type theorems; Hall-MHD equations; MHD equations; GLOBAL WELL-POSEDNESS; NAVIER-STOKES; MAGNETOHYDRODYNAMICS SYSTEM; EXISTENCE; DENSITY; REGULARITY;

D O I：

10.1007/s43037-022-00236-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present paper is devoted to the Liouville-type problem for the three-dimensional stationary incompressible inhomogeneous MHD and Hall-MHD equations without any integrability condition for (del u,del B). More precisely, we show that the velocity fieldu and the magnetic field B, satisfying some suitable growth conditions at infin-ity for the mean oscillations of the potential functions, are identically equal to zero provided that the density rho is essentially bounded.

引用

页数：33

共 48 条

[1] KINETIC FOR MULATION AND GLOBAL EXISTENCE FOR THE HALL-MAGNETO-HYDRODYNAMICS SYSTEM [J].

Acheritogaray, Marion ;

Degond, Pierre ;

Frouvelle, Amic ;

Liu, Jian-Guo .

[2] A Regularity Criterion for the 3D Density-Dependent MHD Equations [J].

Alghamdi, Ahmad Mohammad ;

Gala, Sadek ;

Ragusa, Maria Alessandra ;

Zhang, Zujin .

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2021, 52 (02) :241-251

[3]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[4] Global well-posedness of the 3D incompressible MHD equations with variable density [J].

Bie, Qunyi ;

Wang, Qiru ;

Yao, Zheng-an .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2019, 47 :85-105

[5]

Chae D, 2022, Z ANGEW MATH PHYS, V73, DOI 10.1007/s00033-022-01701-3

[6] On Liouville type theorems for the stationary MHD and Hall-MHD systems [J].

Chae, Dongho ;

Wolf, Jorg .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 295 :233-248

[7] LIOUVILLE TYPE THEOREMS FOR THE STEADY AXIALLY SYMMETRIC NAVIER-STOKES AND MAGNETOHYDRODYNAMIC EQUATIONS [J].

Chae, Dongho ;

Weng, Shangkun .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (10) :5267-5285

[8] Well-posedness for Hall-magnetohydrodynamics [J].

Chae, Dongho ;

Degond, Pierre ;

Liu, Jian-Guo .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (03) :555-565

[9] Liouville-Type Theorems for the Forced Euler Equations and the Navier-Stokes Equations [J].

Chae, Dongho .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2014, 326 (01) :37-48

[10] Remarks on Liouville-Type Theorems for the Steady MHD and Hall-MHD Equations [J].

Chen, Xiaomeng ;

Li, Shuai ;

Wang, Wendong .

JOURNAL OF NONLINEAR SCIENCE, 2022, 32 (01)

← 1 2 3 4 5 →