Related papers: Non-uniform decay of MHD equations with and withou…
In the magnetic diffusion problem, a magnetic diffusion equation is coupled by an Ohmic heating energy equation. The Ohmic heating can make the magnetic diffusion coefficient (i. e., the resistivity) vary violently, and make the diffusion a…
In this paper we consider the problem of a steady MHD flow of a non-Newtonian power-law and electrically conducting fluid in presence of an applied magnetic field. The boundary layer equations are solved in similarity form via the Lyapunov…
In this article, we verify the low Mach number limit of strong solutions to the non-isentropic compressible magnetohydrodynamic equations with zero magnetic diffusivity and ill-prepared initial data in three-dimensional bounded domains,…
We prove the existence of strong time-periodic solutions and their asymptotic stability with the total energy of the perturbations decaying to zero at an exponential decay rate as $t \rightarrow \infty$ for a semilinear (nonlinearly…
The evolution of electromagnetic and thermodynamic fields in a non-ideal fluid are studied in the framework of ultrarelativistic transverse magnetohydrodynamics (MHD), which is essentially characterized by electric and magnetic fields being…
We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor's conjecture, this proves that there exist…
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.…
We present three-dimensional solutions of the magnetohydrostatic equations in the co-rotating frame of reference outside a magnetized rigidly rotating cylinder. We make no symmetry assumption for the magnetic field, but to be able to make…
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…
Within the context of a viscoresistive magnetohydrodynamic (MHD) model with anisotropic heat transport and cross-field mass diffusion, we introduce novel three-term representations for the magnetic field (background vacuum field, field line…
In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this…
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…
This paper investigates the existence and uniqueness of local strong solutions to the three-dimensional compressible magnetohydrodynamic (MHD) equations with density-dependent viscosities in an exterior domain. The system models the…
This paper mainly focus on optimal time decay estimation for large-solution about compressible magnetohydrodynamic equations in 3D whole space, provided that $(\sigma_{0}-1,u_{0},M_{0})\in L^1\cap H^2$. In [2](Chen et al.,2019), they proved…
This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when $\alpha+\beta=1+\frac{n}{2}$ satisfying…
Decaying electron magnetohydrodynamic (EMHD) turbulence in three dimensions is studied via high-resolution numerical simulations. The resulting energy spectra asymptotically approach a k^{-2} law with increasing R_B, the ratio of the…
In this paper we are concerned with the global well-posedness of solutions to magnetohydrodynamics (MHD) boundary layer equations in analytic function spaces. When the initial data is a small perturbation around a selected profile, and such…
A new fully discrete linearized $H^1$-conforming Lagrange finite element method is proposed for solving the two-dimensional magneto-hydrodynamics equations based on a magnetic potential formulation. The proposed method yields numerical…
Whether the smooth solution of the multi-dimensional viscous compressible fluids will blow-up in finite time has always been a chanllenging problem. In the recent work\cite{FM}, Merle et al. proved that there are smooth solutions to the 2D…
The axisymmetric kinematic dynamo problem is reconsidered and a number of open questions are answered. Apart from axisymmetry and smoothness of data and solution we deal with this problem under quite general conditions, i.e. we assume a…