Related papers: A three-dimensional reduced MHD model consistent w…
We propose and analyze a new method for the unsteady incompressible magnetohydrodynamics equations on convex domains with hybrid approximations of both vector-valued and scalar-valued fields. The proposed method is convection-semirobust,…
A new class of analytical 2-D solutions of the full set of the steady magnetohydrodynamic (MHD) equations, describing an axisymmetric helicoidal magnetized outflow originating from a rotating central object, is presented. The solutions are…
A high-fidelity finite volume scheme based on the BVD (boundary variation diminishing) concept is proposed in this study to solve the ideal magnetohydrodynamics (MHD) equations. A hybrid spatial reconstruction profile, consisting of a…
On the basis of simple principles we derive and investigate the equations of relativistic plasma magnetohydrodynamics (MHD) in an arbitrary gravitational field. An exact solution describing the motion of magnetoactive plasma against the…
We consider viscous free-boundary magnetohydrodynamics(MHD) under vacuum in $\mathbb{R}^3$, especially when vacuum magnetic field is identically zero. It is a central problem in mathematics to perform vanishing viscosity limit to get a…
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…
Compressible vortex sheets are fundamental waves in entropy solutions to the multidimensional hyperbolic systems of conservation laws. For the Euler equations in 2-D gas dynamics, the classical linearized stability analysis on compressible…
In this paper, we derive a new shallow asymptotic model for the free boundary plasma-vacuum problem governed by the magnetohydrodynamic equation, vital in describing large-scale processes in flows of astrophysical plasma. More precisely, we…
The theory of mean field electrodynamics for diffusive processes in Electron Magnetohydrodynamic (EMHD) model is presented. In contrast to Magnetohydrodynamics (MHD) the evolution of magnetic field here is governed by a nonlinear equation…
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…
We present a meshless method for magnetohydrodynamics by evolving the vector potential of magnetic fields. A novel scheme and numerical techniques are developed to restrict the divergence of magnetic field, based on the Meshless Finite…
In the presence of a strong uniform magnetic field, we study the influence of space noncommutativity on the electromagnetic waves propagating through a quasi-static homogeneous plasma. In this treatment, we have adopted a physical model…
Smoothed particle magnetohydrodynamics has reached a level of maturity that enables the study of a wide range of astrophysical problems. In this review, the numerical details of the modern SPMHD method are described. The three fundamental…
The constraint of incompressibility is often used to simplify the magnetohydrodynamic (MHD) description of linearized plasma dynamics because it does not affect the ideal MHD marginal stability point. In this paper two methods for…
We present a four-field Virtual Element discretization for the time-dependent resistive Magnetohydrodynamics equations in three space dimensions, focusing on the semi-discrete formulation. The proposed method employs general polyhedral…
In this paper, we establish the global well-posedness of the incompressible magnetohydrodynamics (MHD) system on $n-$dimensional $(n\geq 2)$ periodic boxes with either no magnetic diffusivity (non-resistive case) or no fluid viscosity…
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…
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white…
A Finite Volume (FV) scheme is developed for solving the extended magnetohydrodynamic (XMHD) equations, yielding accurate results in the ideal, resistive, and Hall MHD limits. This is accomplished by first re-writing the XMHD equations such…
We study the linear magnetohydrodynamic (MHD) equations, both in the Newtonian and the general-relativistic limit, as regards a viscous magnetized fluid of finite conductivity and discuss instability criteria. In addition, we explore the…