Related papers: Global well-posedness for Deconvolution Magnetohyd…
In this paper, we study the existence of strong solutions to the two-phase magnetohydrodynamic equations in a bounded domain $\Omega\subseteq \mathbb{R}^3$. The fluids are incompressible, viscous, and resistive. The surface tension is…
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…
In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that…
This paper concerns the Cauchy problem of the nonhomogeneous incompressible magnetohydrodynamic (MHD) equations on the whole two-dimensional (2D) space with vacuum as far field density. In particular, the initial density can have compact…
Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics…
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…
A main result of this paper establishes the global stability of the three-dimensional MHD equations near a background magnetic field with mixed fractional partial dissipation with $\alpha, \beta\in(\frac{1}{2}, 1]$. Namely, the velocity…
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $…
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…
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…
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…
In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In…
High-energy astrophysical systems and compact objects are frequently modeled using ideal relativistic magnetohydrodynamic (MHD) or force-free electrodynamic (FFE) simulations, with the underlying assumption that the discretisation from the…
Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of…
We consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of…
Whether or not the solution to the $2\frac{1}{2}$-dimensional Hall-magnetohydrodynamics system starting from smooth initial data preserves its regularity for all time remains a challenging open problem. Although the research direction on…
We study the long time asymptotic behavior of the inviscid magnetohydrodynamic equations with magnetic dissipation near a combination of Couette flow and a constant magnetic field. Here we show that there exist nearby explicit global in…
This paper establishes a regularity theory for the magnetohydrodynamics (MHD) equations with external forces through scaling analysis. Inspired by the existing methodology, we utilize linearized approximations and the monotonicity property…
At the zero temperature limit, a one-dimensional steady solution to the hydrodynamic equation of a U(2) invariant superfluid is obtained. This solution reveals that the magnitude of magnetization is always directly proportional to the…
In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, i.e., with periodic boundary conditions. We work…