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Related papers: Global current-vortex sheets in the two-dimensiona…

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In this paper, we validate the boundary layer theory for 2D steady viscous incompressible magnetohydrodynamics (MHD) equations in a domain $\{(X, Y)\in[0, L]\times\mathbb{R}_+\}$ under the assumption of a moving boundary at $\{Y=0\}$. The…

Analysis of PDEs · Mathematics 2020-09-15 Shijin Ding , Zhijun Ji , Zhilin Lin

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

We prove the incompressible limit of compressible ideal magnetohydrodynamic(MHD) flows in a reference domain where the magnetic field is tangential to the boundary. Unlike the case of transversal magnetic fields, the linearized problem of…

Analysis of PDEs · Mathematics 2025-02-10 Jiawei Wang , Junyan Zhang

This paper focuses on the 2D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a periodic domain. We present a systematic approach to establishing the global existence of smooth solutions when the initial data…

Analysis of PDEs · Mathematics 2022-06-22 Jiahong Wu , Yi Zhu

It is well known that the nonlinear evolution of magnetohydrodynamic (MHD) turbulence generates current sheets. In the solar wind turbulence, current sheets are frequently observed and they are believed to be an important pathway for the…

Solar and Stellar Astrophysics · Physics 2026-03-19 Chen Shi , Marco Velli , Nikos Sioulas , Zijin Zhang

Physical experiments and numerical simulations have revealed a remarkable stabilizing phenomenon: a background magnetic field stabilizes and dampens electrically conducting fluids. This paper provides a rigorous mathematical justification…

Analysis of PDEs · Mathematics 2025-10-29 Qunyi Bie , Hui Fang , Yanping Zhou

The paper is concerned with the free boundary problem for 2D current-vortex sheets in ideal incompressible magneto-hydrodynamics near the transition point between the linearized stability and instability. In order to study the dynamics of…

Analysis of PDEs · Mathematics 2016-01-15 Alessandro Morando , Paolo Secchi , Paola Trebeschi

This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides…

Analysis of PDEs · Mathematics 2024-02-16 Xiaoping Zhai

We consider a free boundary problem for the incompressible ideal magnetohydrodynamic equations that describes the motion of the plasma in vacuum. The magnetic field is tangent and the total pressure vanishes along the plasma-vacuum…

Analysis of PDEs · Mathematics 2016-09-23 Xumin Gu , Yanjin Wang

In this paper, we consider the three-dimensional full compressible viscous non-resistive MHD system. Global well-posedness is proved for an initial-boundary value problem around a strong background magnetic field. It is also shown that the…

Analysis of PDEs · Mathematics 2022-03-09 Yang Li

This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant…

Analysis of PDEs · Mathematics 2026-05-22 Yi Zhu

We consider the free boundary problem for the plasma-vacuum interface in ideal compressible magnetohydrodynamics (MHD). In the plasma region the flow is governed by the usual compressible MHD equations, while in the vacuum region we…

Analysis of PDEs · Mathematics 2015-06-12 Paolo Secchi , Yuri Trakhinin

A global existence result is established for a free boundary problem of planar magnetohydrodynamic fluid flows with radiation and large initial data. Particularly, it is novelty to embrace the constant transport coefficient. As a…

Analysis of PDEs · Mathematics 2011-10-28 Xulong Qin , Zheng-an Yao

This paper aims to establish the global well-posedness of the free boundary problem for the incompressible viscous resistive magnetohydrodynamic (MHD) equations. Under the framework of Lagrangian coordinates, a unique global solution exists…

Analysis of PDEs · Mathematics 2024-08-29 Wei Zhang , Jie Fu , Chengchun Hao , Siqi Yang

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

In this paper, we investigate the convergence rates of inviscid limits for the free-boundary problems of the incompressible magnetohydrodynamics (MHD) with or without surface tension in $\mathbb{R}^3$, where the magnetic field is…

Analysis of PDEs · Mathematics 2020-01-08 Pengfei Chen , Shijin Ding

It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…

Fluid Dynamics · Physics 2023-06-14 F. Lam

We study the free boundary problem for a plasma-vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement when the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, to better…

Analysis of PDEs · Mathematics 2020-07-15 Alessandro Morando , Paolo Secchi , Yuri Trakhinin , Paola Trebeschi

We consider the motion of two inviscid, compressible, and electrically conducting fluids separated by an interface across which there is no fluid flow in the presence of surface tension. The magnetic field is supposed to be nowhere…

Analysis of PDEs · Mathematics 2022-02-25 Yuri Trakhinin , Tao Wang

We consider the plasma-vacuum interface problem in a horizontally periodic slab impressed by a uniform non-horizontal magnetic field. The lower plasma region is governed by the incompressible inviscid and resistive MHD, the upper vacuum…

Analysis of PDEs · Mathematics 2021-12-17 Yanjin Wang , Zhouping Xin