English
Related papers

Related papers: Global small solution to the 2D MHD system with a …

200 papers

We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…

Analysis of PDEs · Mathematics 2019-08-09 Chengfei Ai , Zhong Tan , Jianfeng Zhou

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 full compressible, viscous, non-resistive MHD system under the assumption that the fluids move on a plane while the magnetic field is oriented vertically. Within the framework of Besov spaces, by introducing…

Analysis of PDEs · Mathematics 2024-08-15 Xiaoping Zhai , Shunhang Zhang

This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the global stability of perturbations near the steady solution given by a…

Analysis of PDEs · Mathematics 2019-06-13 Jiahong Wu , Yi Zhu

In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and…

Analysis of PDEs · Mathematics 2014-10-24 Ting Zhang

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

In this paper, we establish the global existence to the three-dimensional incompressible Hall-MHD equations for a class of large initial data, whose $L^{\infty}$ norms can be arbitrarily large. In addition , we give an example to show that…

Analysis of PDEs · Mathematics 2019-06-11 Jinlu Li , Xing Wu

In this paper, the global smooth solution of Cauchy's problem of incompressible, resistive, viscous Hall-magnetohydrodynamics (Hall-MHD) is studied. By exploring the nonlinear structure of Hall-MHD equations, a class of large initial data…

Analysis of PDEs · Mathematics 2021-04-29 Huali Zhang

In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by $(-\Delta)^{\alpha}$ and magnetic diffusion given by reducing about logarithmic diffusion…

Analysis of PDEs · Mathematics 2023-03-31 Chao Deng , Zhuan Ye , Baoquan Yuan , Jiefeng Zhao

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

Whether or not the classical solutions of the two-dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only Laplacian magnetic diffusion (without velocity dissipation) are globally well-posed is a difficult problem and…

Analysis of PDEs · Mathematics 2023-03-31 Zhuan Ye

The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is…

Analysis of PDEs · Mathematics 2025-05-08 Jiahong Wu , Xiaoping Zhai

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…

Analysis of PDEs · Mathematics 2019-07-02 Yang Li , Yongzhong Sun

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

In recent years, the global existence of classical solutions to the Cauchy problem for 2D incompressible viscous MHD equations without magnetic diffusion has been proved in \cite{Ren,TZhang}, under the assumption that initial data is close…

Analysis of PDEs · Mathematics 2025-05-22 Shijin Ding , Ronghua Pan , Yi Zhu

We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global…

Analysis of PDEs · Mathematics 2015-04-28 Maicon J. Benvenutti , Lucas C. F. Ferreira

We prove the global well-posedness of the 2D incompressible non-resistive MHD equations with a velocity damping term near the non-zero constant background magnetic field. To this end, we newly design a normal mode method of effectively…

Analysis of PDEs · Mathematics 2022-10-20 Min Jun Jo , Junha Kim , Jihoon Lee

In this paper, we are concerned with the 2D damped wave-type magnetohydrodynamic system (abbreviated as MHD-wave system). The purpose of this paper is to study the large time behavior of solutions to the MHD-wave system, espesically to…

Analysis of PDEs · Mathematics 2024-11-05 Yaowei Xie , Huan Yu

This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in…

Analysis of PDEs · Mathematics 2021-02-16 Fei Jiang , Song Jiang

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