Related papers: The axisymmetric antidynamo theorem revisited
To explain the large-scale magnetic field of the Sun and other bodies, mean-field dynamo theory is commonly applied where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the…
The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the…
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…
An inhomogeneous fluid in accelerated motion is investigated. When the velocity field $v(x)$ is not constant, the geometry viewed by a static observer is curved, as if the observer were immersed in a gravitational field. A…
We study the collective excitations in a dissipative charged fluid at zero chemical potential when an external magnetic field is present. While in the absence of magnetic field, four collective excitations appear in the fluid, we find five…
We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the…
The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is slaved to the forcing. The forcing…
In this article we revisit the significance of the often debated structural similarity between the equations of electromagnetism and fluid dynamics. Although the matching of the two sets of equations has successfully been done for…
We consider a free-boundary problem for the incompressible elastodynamics describing the motion of an elastic medium in a periodic domain with a moving boundary and a fixed bottom under the influence of surface tension. The local…
The influence of fluctuating conductivity on the coefficients known from the mean-field electrodynamics is considered. If the conductivity fluctuations are assumed as uncorrelated with the turbulent velocity field then only the effective…
With materials of anisotropic electrical conductivity, it is possible to generate a dynamo with a simple velocity field, of the type precluded by Cowling's theorems with isotropic materials. Following a previous study by Ruderman and…
We consider a 2D incompressible and electrically conducting fluid in the domain $\mathbb{T}\times\mathbb{R}$. The aim is to quantify stability properties of the Couette flow $(y,0)$ with a constant homogenous magnetic field $(\beta,0)$ when…
The popular demonstration involving a permanent magnet falling through a conducting pipe is treated as an axially symmetric boundary value problem. Specifically, Maxwell's equations are solved for an axially symmetric magnet moving…
We use spherical coordinates to devise a new exact solution to the governing equations of geophysical fluid dynamics for an inviscid and incompressible fluid with a general density distribution and subjected to forcing terms. The latter are…
In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has…
We consider singularities in the ElectroHydroDynamic equations. In a regime where we are allowed to neglect surface tension, and assuming that the free surface is given by an injective curve and that either the fluid velocity or the…
We study stationary free boundary configurations of an ideal incompressible magnetohydrodynamic fluid possessing nested flux surfaces. In 2D simply connected domains, we prove that if the magnetic field and velocity field are never…
We present an exact solution to the problem of a self-consistent equilibrium force-free magnetic flux rope. Unlike other approaches, we use magnetostatic equations and assume only a relatively rapid decrease in the axial magnetic field at…
We consider a fluid dynamo model generated by the flow on both sides of a moving layer. The magnetic permeability of the layer is larger than that of the flow. We show that there exists an optimum value of magnetic permeability for which…
We discuss the well-posedness of the 'transient eddy current' magneto-quasistatic approximation of Maxwell's initial value problem with bounded and measurable conductivity, with sources, on a domain. We prove existence and uniqueness of…