相关论文: On Moffatt's magnetic relaxation equations

We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic…

This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…

This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides…

Motter et al. derived a real-valued master stability function which determines whether and to what degree a given power grid is asymptotically stable. Stright and Edrington adopted certain uniformity assumptions on a grid's components and…

In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…

In this note, we show that there exist solutions of the Muskat problem that shift stability regimes: they start unstable, then become stable, and finally return to the unstable regime. We also exhibit numerical evidence of solutions with…

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…

We study the linear and nonlinear stability of relative equilibria in the planar N-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological…

This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…

We present two results related to magnetized Vlasov equations. Our first contribution concerns the stability of solutions to the magnetized Vlasov-Poisson system with a non-uniform magnetic field using the optimal transport approach…

In [25], Moffatt introduced the concept of helicity in an inviscid fluid and examined the helicity preservation of smooth solution to barotropic compressible flow. In this paper, it is shown that the weak solutions of the above system in…

Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable…

In previous work constant magnetic field strength solutions for SU(2) gauge theory on a torus were found, which somewhat surprisingly turned out to be classically stable. This was called marginal stability, as moving along one of its…

We study the stability of a type of stratified flows of the two dimensional inviscid incompressible MHD equations with velocity damping. The exponential stability for the perturbation near certain stratified flow is investigated in a…

A detailed stability analysis is presented for the de Sitter solution with a homogeneous magnetic field that was recently found in the context of a $U(1)$ gauge theory nonminimally coupled to scalar-tensor gravity. The magnetic field is…

Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded domain. One phase is assumed to be magnetic, the other phase…

Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive theories such as Taylor relaxation preserve only global…

We consider in this paper the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem re-writes as an abstract evolution equation and we use this property to prove…

Monte Carlo simulations are used to study the magnetic relaxation of a system of single domain particles with dipolar interactions modeled by a chain of Heisenberg classical spins. We show that the so-called $T\ln(t/\tau_0)$ method can be…

Because different constraints are imposed, stability conditions for dissipationless fluids and magnetofluids may take different forms when derived within the Lagrangian, Eulerian (energy-Casimir), or dynamical accessible frameworks. This is…