The global existence and analyticity of a mild solution to the 3D regularized MHD equations

被引：1

作者：

Xiao, Cuntao ^{[1
]}

Qiu, Hua ^{[2
]}

Yao, Zheng-an ^{[3
]}

机构：

[1] Guangdong Univ Technol, Sch Math & Stat, Guangzhou 510090, Peoples R China

[2] South China Agr Univ, Dept Math, Guangzhou 510642, Peoples R China

[3] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

来源：

ACTA MATHEMATICA SCIENTIA | 2024年 / 44卷 / 03期

基金：

中国国家自然科学基金;

关键词：

regularized MHD equations; fractional Laplacian; global well-posedness; analyticity; decay rate; LEI-LIN SOLUTION; WELL-POSEDNESS; CAUCHY-PROBLEM; ALPHA MODEL; DECAY;

D O I：

10.1007/s10473-024-0311-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms. We establish the global existence of mild solutions to this system with small initial data. In addition, we also obtain the Gevrey class regularity and the temporal decay rate of the solution.

引用

页码：973 / 983

页数：11

共 24 条

[1] EXISTENCE AND ANALYTICITY OF LEI-LIN SOLUTION TO THE NAVIER-STOKES EQUATIONS [J].

Bae, Hantaek .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 143 (07) :2887-2892

[2] Large time behaviour of solutions to the 3D-NSE in Xσ spaces [J].

Benameur, Jamel ;

Bennaceur, Mariem .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2020, 482 (02)

[3] Long time decay to the Lei-Lin solution of 3D Navier-Stokes equations [J].

Benameur, Jamel .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 422 (01) :424-434

[4] Finite Dimensional Global Attractor for 3D MHD-α Models: A Comparison [J].

Catania, Davide .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2012, 14 (01) :95-115

[5] Camassa-Holm equations as a closure model for turbulent channel and pipe flow [J].

Chen, S ;

Foias, C ;

Holm, DD ;

Olson, E ;

Titi, ES ;

Wynne, S .

PHYSICAL REVIEW LETTERS, 1998, 81 (24) :5338-5341

[6] Global well-posedness of the Cauchy problem for certain magnetohydrodynamic-α models [J].

Du, Yi ;

Qiu, Hua ;

Zhengan-Yao .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 33 (13) :1545-1557

[7] Global Cauchy Problem for the 2-D Magnetohydrodynamic-α Models with Partial Viscous Terms [J].

Fan, Jishan ;

Ozawa, Tohru .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2010, 12 (02) :306-319

[8] REGULARITY CRITERIA FOR THE MAGNETOHYDRODYNAMIC EQUATIONS WITH PARTIAL VISCOUS TERMS AND THE LERAY-α-MHD MODEL [J].

Fan, Jishan ;

Ozawa, Tohru .

[9] Averaged Lagrangians and the mean effects of fluctuations in ideal fluid dynamics [J].

Holm, DD .

PHYSICA D-NONLINEAR PHENOMENA, 2002, 170 (3-4) :253-286

[10] Global Mild Solutions of Navier-Stokes Equations [J].

Lei, Zhen ;

Lin, Fanghua .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (09) :1297-1304

← 1 2 3 →