Related papers: The axisymmetric antidynamo theorem revisited
We study the long-time behavior of global strong solutions to a hydrodynamic system for nonhomogeneous incompressible nematic liquid crystal flows driven by two types of external forces in a smooth bounded domain in $\mathbb{R}^2$. For…
We consider a viscous incompressible fluid below the air and above a fixed bottom. The fluid dynamics is governed by the gravity-driven incompressible Navier-Stokes equations, and the effect of surface tension is neglected on the free…
We construct a magnetic helicity conserving dynamo theory which incorporates a calculated magnetic helicity current. In this model the fluid helicity plays a small role in large scale magnetic field generation. Instead, the dynamo process…
We study magnetic field evolution in flows with fluctuating in time governing parameters in electrically conducting fluid. We use a standard mean-field approach to derive equations for large-scale magnetic field for the fluctuating ABC-flow…
We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot…
The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated…
We consider dissipative relativistic fluid theories on a fixed flat, compact, globally hyperbolic, Lorentzian manifold. We prove that for all initial data in a small enough neighborhood of the equilibrium states (in an appropriate Sobolev…
We are investigating numerically the non-linear behavior of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small…
In this paper, we consider the quasi-neutral limit of a three dimensional Euler-Poisson system of compressible fluids coupled to a magnetic field. We prove that, as Debye length tends to zero, periodic initial-value problems of the model…
We consider the dynamics of a layer of an incompressible electrically conducting fluid interacting with the magnetic field in a two-dimensional horizontally periodic setting. The upper boundary is in contact with the atmosphere, and the…
This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields. We consider an initial-boundary value problem for both compressible and…
Astrophysical objects with negligible resistivity are often threaded by large scale magnetic fields. The generation of these fields is somewhat mysterious, since a magnetic field in a perfectly conducting fluid cannot change the flux…
We consider weak (''Leray'') solutions to the stationary Navier-Stokes system with Oseen and rotational terms, in an exterior domain. It is shown the velocity may be split into a constant times the first column of the fundamental solution…
We consider the problem of motion of several rigid bodies immersed in a perfect compressible fluid. Using the method of convex integration we establish the existence of infinitely many weak solutions with {\it a priori} prescribed motion of…
The small-scale dynamo is typically studied by assuming that the correlation time of the velocity field is zero. Some authors have used a smooth renovating flow model to study how the properties of the dynamo are affected by the correlation…
An exact analytic solution has been obtained for a uniformly expanding, neutral, infinitely conducting plasma cylinder in an external uniform and constant magnetic field. The electrodynamical aspects related to the emission and…
The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…
Axisymmetric equilibria with incompressible flows of arbitrary direction are studied in the framework of magnetohydrodynamics under a variety of physically relevant side conditions. To this end a set of pertinent non-linear ODEs are…
The self-excitation of magnetic field by a spiral Couette flow between two coaxial cylinders is considered. We solve numerically the fully nonlinear, three-dimensional MHD equations for magnetic Prandtl numbers Pm (ratio of kinematic…
In this article we will introduce a new model to describe the leading order behavior of an ideal and axisymmetric fluid moving in a very narrow domain. After providing a formal derivation of the model, we will prove the well-posedness and…