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We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a…

Analysis of PDEs · Mathematics 2015-09-28 Renhui Wan

This paper focuses on the global stability of the 3D magneto-micropolar equations with partial viscosity in the torus $\mathbb T^3$. We first establish the global stability and exponential decay for the 3D magneto-micropolar equations with…

Analysis of PDEs · Mathematics 2026-03-04 Haifeng Shang

Whether or not smooth solutions to the 3D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion are always global in time remains an extremely challenging open problem. No global well-posedness or stability result is…

Analysis of PDEs · Mathematics 2023-07-19 Jiahong Wu , Xiaoping Zhai

In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…

Analysis of PDEs · Mathematics 2025-12-30 Hui Fang , Pingping Gui , Yanping Zhou

In this paper, we consider the Cauchy problem of the two-dimensional regularized incompressible magnetohydrodynamics equations. The main objective of this paper is to establish the global regularity of classical solutions of the…

Analysis of PDEs · Mathematics 2019-09-09 Zhuan Ye

This paper solves the global conormal regularity problem for the three-dimensional incompressible MHD equations with slip boundary condition near a background magnetic field. Motivated by applications in geophysics, the MHD system…

Analysis of PDEs · Mathematics 2025-07-01 Jincheng Gao , Jiahong Wu , Zheng-an Yao , Xuan Yin

We study the Cauchy problem for the three-dimensional isentropic compressible ideal (inviscid and non-resistive) magnetohydrodynamic equations with velocity damping on the periodic torus $\mathbb{T}^3$. The system admits a steady…

Analysis of PDEs · Mathematics 2026-05-07 Liening Qiao , Jiahong Wu , Fuyi Xu , Xiaoping Zhai

We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…

Analysis of PDEs · Mathematics 2016-03-29 Ling-Bing He , Li Xu , Pin Yu

This paper resolves the global regularity problem for the three-dimensional incompressible magnetohydrodynamics (MHD) equations in the upper half-space with slip boundary conditions, in the presence of a background magnetic field. Motivated…

Analysis of PDEs · Mathematics 2025-08-14 Jincheng Gao , Lianyun Peng , Jiahong Wu , Zheng-an Yao

A main result of this paper establishes the global stability of the 3D MHD equations with mixed partial dissipation near a background magnetic field in the domain $\Omega=\mathbb{T}^2\times\mathbb{R}$ with $\mathbb{T}^2=[0, 1]^2$. More…

Analysis of PDEs · Mathematics 2024-02-05 Xuemin Deng , Yuelong Xiao , Aibin Zang

Whether the global existence and uniqueness of strong solutions of $n$-dimensional incompressible magnetohydrodynamic (MHD for short) equations with only kinematic viscosity or magnetic diffusion holds true or not remains an outstanding…

Analysis of PDEs · Mathematics 2024-02-19 Yaowei Xie , Quansen Jiu , Jitao Liu

This paper solves the global well-posedness and stability problem on a special $2\frac12$-D compressible viscous non-resistive MHD system near a steady-state solution. The steady-state here consists of a positive constant density and a…

Analysis of PDEs · Mathematics 2022-11-11 Boqing Dong , Jiahong Wu , Xiaoping Zhai

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…

Analysis of PDEs · Mathematics 2012-04-26 Dongfen Bian , Boling Guo

We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation…

Analysis of PDEs · Mathematics 2024-08-23 Yang Liu , Xin Zhong

The main objective of this paper is to study the global strong solution of the parabolic-hyperbolic incompressible magnetohydrodynamic (MHD) model in two dimensional space. Based on Agmon, Douglis and Nirenberg's estimates for the…

Analysis of PDEs · Mathematics 2017-01-31 Ruikuan Liu , Jiayan Yang

We consider the Cauchy problem to the three-dimensional isentropic compressible Magnetohydrodynamics (MHD) system with density-dependent viscosities. When the initial density is linearly equivalent to a large constant state, we prove that…

Analysis of PDEs · Mathematics 2024-08-20 Yachun Li , Peng Lu , Zhaoyang Shang

In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…

Analysis of PDEs · Mathematics 2026-02-05 Huali Zhang

In this paper, we study the global well-posedness and decay rates of strong solutions to an incompressible Vlasov-MHD model arising in magnetized plasmas. This model is consist of the Vlasov equation and the incompressible…

Analysis of PDEs · Mathematics 2024-08-27 Fucai Li , Jinkai Ni , Man Wu

We revisit the 2D Cauchy problem of nonhomogeneous heat conducting magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. For the initial density allowing vacuum at infinity, we derive the global existence and uniqueness of strong solutions…

Analysis of PDEs · Mathematics 2022-01-05 Xin Zhong

This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to…

Analysis of PDEs · Mathematics 2017-08-08 Boqiang Lv , Zhonghai Xu , Xin Zhong