Related papers: Topological Invariants in Higher-Dimensional Magne…
The equations of 2D incompressible dissipationless extended magnetohydrodynamics (XMHD) extend the equations of incompressible Hall MHD (HMHD) by retaining finite-electron inertia. These XMHD equations couple the fluid velocity ${\bf V} =…
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…
Helicity, a measure of the breakage of reflectional symmetry representing the topology of turbulent flows, contributes in a crucial way to their dynamics and to their fundamental statistical properties. We review several of their main…
We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines changes under the flow. By Alfv\'en's theorem this is known to be…
We show that relativistic magnetohydrodynamics (MHD) can be recast as a novel theory of superfluidity. This new theory formulates MHD just in terms of conservation equations, including dissipative effects, by introducing appropriate…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Newly emerging magnetic flux can show a complicated linked or interwoven topology of the magnetic field. The complexity of this linkage or knottedness of magnetic flux is related to the free energy stored in the magnetic field. Magnetic…
We show that oppositely directed fluxes of energy and magnetic helicity coexist in the inertial range in fully developed magnetohydrodynamic (MHD) turbulence with small-scale sources of magnetic helicity. Using a helical shell model of MHD…
Left- and right-handed helical modes' statistical absolute equilibria appear \textit{separately}. If both chiral sectors present, one can dominate around its positive pole, which is relevant to the nearly maximally helical (force free for…
The nonhomogeneous incompressible Magnetohydrodynamic Equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with slip boundary conditions. The key is the constraint of an additional initial value…
A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint $\divb=0$ for the magnetic field vector $\bb$, is proposed. The…
Through the use of suitable variable transformations, the commonality of all extended magnetohydrodynamics (MHD) models is established. Remarkable correspondences between the Poisson brackets of inertialess Hall MHD and inertial MHD (which…
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits.…
A wide variety of astrophysical phenomena involve the flow of turbulent magnetized gas with relativistic velocity or energy density. Examples include gamma-ray bursts, active galactic nuclei, pulsars, magnetars, micro-quasars, merging…
We show that an infinite number of non-unitary minimal models may describe two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and absence of the Alf'ven effect. We argue that the existence of a critical dynamical…
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabelling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A…
We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The…
In this paper, we are concerned with the energy and magnetic helicity conservation of weak solutions for both the electron and Hall magnetohydrodynamic equations. Various sufficient criteria to ensure the energy and magnetic helicity…
The long-time relaxation of ideal two dimensional magnetohydrodynamic turbulence subject to the conservation of two infinite families of constants of motion---the magnetic and the "cross" topology invariants--is examined. The analysis of…
In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic…