Related papers: Geometric Results for Compressible Magnetohydrodyn…
We prove the existence of both local and global smooth solutions to the Cauchy problem in $\R^3$ for the incompressible magnetohydrodynamics (MHD) system. We also prove that the solution to the incompressible MHD system can be obtained as…
Non-solitonic examples of the application of geometrical and topological methods in plasma physics and magnetohydrodynamics (MHD) are given. The first example considers the generalization of magnetic helicity to gravitational torsion loop.…
We study the local existence of solutions to the magnetohydrodynamics (MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the $L^p-L^q$ class with inhomogeneous boundary conditions. The…
We have written and tested a new general relativistic magnetohydrodynamics (GRMHD) code, capable of evolving MHD fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled…
We prove the local well-posedness of the 3D free-boundary incompressible ideal magnetohydrodynamics (MHD) equations with surface tension, which describe the motion of a perfect conducting fluid in an electromagnetic field. We adapt the…
We derive one dimensional (1D) analytical solutions for the transport equations of incompressible magnetohydrodynamic (MHD) turbulence developed by Zank et al. [2012], Adhikari et al. [2023], including the Els\"asser energies and the…
The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of…
A recent paper considered symmetries and conservation laws of the plane one-dimensional flows for magnetohydrodynamics in the mass Lagrangian coordinates. This paper analyses the one-dimensional magnetohydrodynamics flows with cylindrical…
It is demonstrated that the deformation of magnetic field lines in incompressible magnetohydrodynamic flows results from a compressible mapping. Appearance of zeroes for the mapping Jacobian correspond to the breaking of magnetic field…
We present a new computational method for smoothly matching general relativistic ideal magnetohydrodynamics (MHD) to its force-free limit. The method is based on a flux-conservative formalism for MHD and its force-free limit, and a vector…
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric…
In this work we introduce a novel semi-implicit structure-preserving finite-volume/finite-difference scheme for the viscous and resistive equations of magnetohydrodynamics (MHD) based on an appropriate 3-split of the governing PDE system,…
We investigate the explicit convex relaxation of the ideal magnetohydrodynamics equations. We provide a non-trivial lower estimate on the lamination hull and an upper estimate on the $\Lambda$-convex hull, the latter providing inequalities…
We find two Lax representations for the reduced magnetohydrodynamics equations ({\sc rmhd}) and derive a B{\"a}cklund transformation between the tangent and the cotangent coverings of these equations. Then, we study the action of the…
Hall magnetohydrodynamics (MHD) properties near a two-dimensional (2D) X-type magnetic neutral line in the steady state are considered via heuristic and rigorous developments. Upon considering the steady-state as the asymptotic limit of the…
In this note we propose a trilinear bracket formulation for the Hamiltonian extended Magnetohydrodynamics (XMHD) model with homogeneous mass density. The corresponding two-dimensional representation is derived by performing spatial…
Magnetohydrodynamic (MHD) seismology uses naturally occurring MHD waves to infer plasma properties that are otherwise hard to measure, especially magnetic field strength and topology, electric currents, fine structuring, transport…
We solve the magnetohydrodynamic (MHD) equations governing axisymmetric flows around neutron stars and black holes and found all possible solution topologies for adiabatic accretion. We divide the parameter space spanned by the conserved…
The aim is to justify rigorously the so-called reduced magnetohydrodynamic model (abbreviated as RMHD), which is widely used in fusion, space and astrophysical plasmas. Motivated by physics, the focus is on plasmas that are simultaneously…
Galactic HI is a gas that is coupled to magnetic field because of its fractional ionization. Many properties of HI are affected by turbulence. Recently, there has been a significant breakthrough on the theory of magnetohydrodynamic (MHD)…