Global strong solution for the two-dimensional magnetohydrodynamics equations with shearing-periodic boundary conditions

被引：0

作者：

Kondo, Shintaro ^{[1
]}

Nakamura, Tatsuki ^{[2
]}

机构：

[1] Gifu Univ, Elect & Comp Engn, 1-1 Yanagido, Gifu 5011193, Japan

[2] AISIN Corp, Kariya, Aichi, Japan

来源：

MATHEMATISCHE NACHRICHTEN | 2025年

基金：

日本学术振兴会;

关键词：

MHD equations; shear flows; strong solution; NAVIER-STOKES EQUATIONS; PARABOLIC EQUATIONS; CLASSICAL-SOLUTIONS; EXISTENCE; SYSTEM;

D O I：

10.1002/mana.70012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we investigate the two-dimensional (2D), two-field magnetohydrodynamics (MHD) equations in the presence of a shear flow, assuming positive plasma viscosity and resistivity. We establish the global-in-time existence and uniqueness of a strong solution for the 2D two-field MHD equations under shearing-periodic boundary conditions, as proposed by Hawley et al. Moreover, we establish the existence and uniqueness of a strong solution for the linear advection-diffusion equation under shearing-periodic boundary condition by employing uniformly local L2$L<^>2$ spaces.

引用

页数：28

共 43 条

[31] Investigation into the Dual Role of Shear Flow in 2D MHD Turbulence [J].

Newton, Andrew P. L. ;

Kim, Eun-jin .

PHYSICAL REVIEW LETTERS, 2009, 102 (16)

[32] The drift-diffusion system in two-dimensional critical Hardy space [J].

Ogawa, Takayoshi ;

Shimizu, Senjo .

JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 255 (05) :1107-1138

[33]

Prouse G., 1963, Rend. Sem. Mat. Univ. Padova, V33, P186

[34] Investigation of a Vorticity-preserving Scheme for the Euler Equations [J].

Seligman, Darryl ;

Shariff, Karim .

ASTROPHYSICAL JOURNAL, 2019, 877 (02)

[35] SOME MATHEMATICAL QUESTIONS RELATED TO THE MHD EQUATIONS [J].

SERMANGE, M ;

TEMAM, R .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1983, 36 (05) :635-664

[36]

Solonnikov V. A., 1965, Trudy Mat. Inst. Steklov., V83, P3

[37] Well-posedness of mild solutions to the drift-diffusion and the vorticity equations in amalgam spaces [J].

Suguro, Takeshi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 520 (01)

[38] Magnetohydrodynamics in a cylindrical shearing box [J].

Suzuki, Takeru K. ;

Taki, Tetsuo ;

Suriano, Scott S. .

PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF JAPAN, 2019, 71 (05)

[39] DISK WINDS DRIVEN BY MAGNETOROTATIONAL INSTABILITY AND DISPERSAL OF PROTOPLANETARY DISKS [J].

Suzuki, Takeru K. ;

Inutsuka, Shu-ichiro .

ASTROPHYSICAL JOURNAL LETTERS, 2009, 691 (01) :L49-L54

[40] Uniformly local Lp estimate for 2-D vorticity equation and its application to Euler equations with initial vorticity in bmo [J].

Taniuchi, Y .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 248 (01) :169-186

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