Related papers: On existence of resistive magnetohydrodynamic equi…
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.…
The magnetohydrodynamic dynamo equation is derived within general relativity, using the covariant 1+3 approach, for a plasma with finite electric conductivity. This formalism allows for a clear division and interpretation of plasma and…
We present an extension to the special relativistic, ideal magnetohydrodynamics (MHD) equations, designed to capture effects due to resistivity. The extension takes the simple form of an additional source term which, when implemented…
The quantum hydrodynamic model for charged particle systems is extended to the cases of non zero magnetic fields. In this way, quantum corrections to magnetohydrodynamics are obtained starting from the quantum hydrodynamical model with…
We extend the magnetic connection theorem of ideal magnetohydrodynamics to nonideal relativistic pair plasmas. Adopting a generalized Ohm's law, we prove the existence of generalized magnetofluid connections that are preserved by the plasma…
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…
Condensed matter systems can host emergent `vacua' with particles, fields and dimension different from that of the universe we inhabit. Motivated by the appearance of emergent gauge fields with both electric and magnetic charges, we…
We consider the complete system of equations governing the motion of a general compressible, viscous, electrically and heat conductive fluid driven by non-conservative boundary conditions. We show the existence of a bounded absorbing set in…
The aim of this note is to study the dynamo properties of the magnetohydrodynamics system at vanishing Rm. Improving the analysis of a former study, we shall establish a generic Lyapunov instability result.
Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…
We present the basic equations for stationary, incompressible resistive MHD flows in two dimensions. This leads to a system of differential equations for two flux functions, one elliptic partial differential equation (Grad-Shafranov-like)…
A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the…
We present a new variational formulation for Viscous and resistive Hall Magnetohydrodynamic. We first find a variational principle for ideal HMHD by applying the physical assumptions leading to HMHD at the lagrangian level, and then we add…
With the help of the generalized characteristics(GC) of the first order partial differential equations(PDE) we calculate the differential equation system of characteristics of the homogenous magneto hydrodynamical equations(MHD).
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 consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic viscous and non-resistive magnetohydrodynamic flows. The global well-posedness of strong solutions with general large data is…
We clarify how magnetic reconnection can be derived from magnetohydrodynamics (MHD) equations in a way that is easily understandable to university students. The essential mechanism governing the time evolution of the magnetic field is…
In this article, we study the stability and large time behavior for an multi-dimensional incompressible magnetohydrodynamical system with a velocity damping term, for small perturbations near a steady-state of magnetic field fulfilling the…
In this article we consider the stability threshold of the 2D magnetohydrodynamics (MHD) equations near a combination of Couette flow and large constant magnetic field. We study the partial dissipation regime with full viscous and only…
We define a dissipative measure-valued (DMV) solution to the system of equations governing the motion of a general compressible, viscous, electrically and heat conducting fluid driven by non-conservative boundary conditions. We show the…