English
Related papers

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

200 papers

We show local existence and uniqueness of plasma(fluid)-vaccum free boundary problem of magnetohydrodynamic flow in three-dimensional space with infinite depth setting when magnetic field is zero on the free boundary. We use…

Analysis of PDEs · Mathematics 2017-10-09 Donghyun Lee

The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role…

Plasma Physics · Physics 2018-10-24 Chuanfei Dong , Liang Wang , Yi-Min Huang , Luca Comisso , Amitava Bhattacharjee

We study the global stability of large solutions to the compressible isentropic magnetohydrodynamic equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the solutions converge to an…

Analysis of PDEs · Mathematics 2025-10-17 Yang Liu , Guochun Wu , Xin Zhong

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando--Trebeschi (2008) [20]. The…

Analysis of PDEs · Mathematics 2020-09-24 Alessandro Morando , Paola Trebeschi , Tao Wang

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the…

Plasma Physics · Physics 2015-06-05 M. E. Brachet , M. D. Bustamante , G. Krstulovic , P. D. Mininni , A. Pouquet , D. Rosenberg

In this paper, the existence of finite-time splash singularity is proved for the free-boundary problem of the viscous and non-resistive incompressible magnetohydrodynamic (MHD) equations in $ \mathbb{R}^{3}$, based on a construction of a…

Analysis of PDEs · Mathematics 2023-09-19 Guangyi Hong , Tao Luo , Zhonghao Zhao

We study the possibility of constructing steady magnetic fields satisfying the force balance equation of ideal magnetohydrodynamics with tangential boundary conditions in asymmetric confinement vessels, i.e. bounded regions that are not…

Plasma Physics · Physics 2020-12-22 Naoki Sato

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

We investigate a steady planar flow of an ideal fluid in a (bounded or unbounded) domain $\Omega\subset \mathbb{R}^2$. Let $\kappa_i\not=0$, $i=1,\ldots, m$, be $m$ arbitrary fixed constants. For any given non-degenerate critical point…

Analysis of PDEs · Mathematics 2022-05-06 Daomin Cao , Guolin Qin , Changjun Zou

The stability of current sheets in collisionless relativistic pair plasma was studied via two-dimensional two-fluid relativistic magnetohydrodynamic simulations with vanishing internal friction between fluids. In particular, we investigated…

High Energy Astrophysical Phenomena · Physics 2016-03-23 Maxim V. Barkov , Serguei S. Komissarov

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 show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the…

Analysis of PDEs · Mathematics 2022-11-03 Xumin Gu , Chenyun Luo , Junyan Zhang

In this paper, we prove the local well-posedness of plasma-vacuum interface problem for ideal incompressible magnetohydrodynamics under the stability condition: the magnetic field $\mathbf{h}$ and the vacuum magnetic field…

Analysis of PDEs · Mathematics 2017-05-02 Yongzhong Sun , Wei Wang , Zhifei Zhang

For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global…

Analysis of PDEs · Mathematics 2024-06-19 Yuebo Cao , Yi Peng , Ying Sun

In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed…

Plasma Physics · Physics 2020-07-15 David Pfefferlé , Lyle Noakes , Yao Zhou

We study the two-dimensional MHD boundary layer equations. For small perturbation around a tangential background magnetic field, we obtain the global-in-time existence and uniqueness of solutions in Sobolev spaces. The proof relies on the…

Analysis of PDEs · Mathematics 2024-09-20 Wei-Xi Li , Zhan Xu , Anita Yang

We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the…

Analysis of PDEs · Mathematics 2021-08-31 Xiufang Cui , Shengxin Li , Feng Xie

We consider the motion of several rigid bodies immersed in a two-dimensional incompressible perfect fluid. The motion of the rigid bodies is given by the Newton laws with forces due to the fluid pressure and the fluid motion is described by…

Analysis of PDEs · Mathematics 2020-07-13 Olivier Glass , József Kolumbán , Franck Sueur

This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\bf{e_1})$ for…

Analysis of PDEs · Mathematics 2024-01-04 Zhaoyun Zhang , Xiaopeng Zhao

The question what information is necessary for determination of a unique solution of hydrodynamic equations for ideal fluid is investigated. Arbitrary inviscid flows of the barotropic fluid and of incompressible fluid are considered. After…

General Physics · Physics 2007-05-23 Yuri A. Rylov