Related papers: Topological Invariants in Higher-Dimensional Magne…
The principles of restricted superposition of circularly polarized arbitrary-amplitude waves for several hydrodynamic type models are illustrated systematically with helical representation in a unified sense. It is shown that the only…
We prove the existence of weak solutions to the 3D ideal MHD equations, of class $C^\alpha$ with $\alpha=1/200$, for which the total energy and the cross helicity (i.e., the so-called Els\"asser energies) are not conserved. The solutions do…
It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…
The purpose of this article is twofold: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in $\mathbb{R}^3$ with initial data $(u_0,b_0)$ of arbitrarily large size in any critical space. To do so,…
We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic…
Isotropic homogeneous hydromagnetic turbulence is studied using numerical simulations at resolutions of up to 1024^3 meshpoints. It is argued that, in contrast to the kinematic regime, the nonlinear regime is characterized by a spectral…
We study the possibility that primordial magnetic fields generated in the transition between inflation and reheating posses magnetic helicity, $H_M$. The fields are induced by stochastic currents of scalar charged particles created during…
We perform direct numerical simulations of three-dimensional freely decaying magnetohydrodynamic (MHD) turbulence. For helical magnetic fields an inverse cascade effect is observed in which power is transfered from smaller scales to larger…
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. In here, the average helicity is derived using the conformally-invariant…
In Lagrangian coordinates, the local well-posedness of low regularity solutions is established for an ideal incompressible magnetohydrodynamic (MHD) system subject to a homogeneous background magnetic field. First, the MHD system is…
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…
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…
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…
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 describe a new approach to triple linking invariants and integrals, aiming for a simpler, wider and more natural applicability to the search for higher order helicities of fluid flows and magnetic fields. To each three-component link in…
The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning…
We study the inverse cascade of magnetic helicity in conducting fluids by investigating the detailed transfer of helicity between different spherical shells in Fourier space in direct numerical simulations of three-dimensional…
A fully geometrical treatment of general relativistic magnetohydrodynamics (GRMHD) is developed under the hypotheses of perfect conductivity, stationarity and axisymmetry. The spacetime is not assumed to be circular, which allows for…
We have carried out simulations of the nonlinear evolution of the magnetohydrodynamic (MHD) Kelvin-Helmholtz (KH) instability for compressible fluids in $2\frac{1}{2}$-dimensions, extending our previous work by Frank et al (1996) and Jones…
We study the transition in dimensionality of a three-dimensional magnetohydrodynamic flow forced only mechanically, when the strength of a magnetic guiding field is gradually increased. We use numerical simulations to consider cases in…