Related papers: Stability of Chandrasekhar's nonlinear force-free …
The structure of steady axisymmetric force-free magnetosphere of a Kerr black hole (BH) is governed by a second-order partial differential equation of $A_\phi$ depending on two "free" functions $\Omega(A_\phi)$ and $I(A_\phi)$, where…
Large-amplitude Alfv\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model…
We find a new family of solutions for force-free magnetic structures in cylindrical geometry. These solutions have radial power-law dependance and are periodic but non-harmonic in azimuthal direction; they generalize the vacuum…
We show that in the presence of a slowly rotating strong transverse magnetic field there is an infinite spectrum of harmonic wave functions $A_n$ due to the first order QED correction (in $\alpha^2$) given by the Euler-Heisenberg…
I report on recent work concerning the existence and stability of self-gravitating spheres with anisotropic pressure. After presenting new exact solutions, Chandrasekhar's variational formalism for radial perturbations is generalized to…
This paper provides a brief overview of the formation of stellar fossil magnetic fields and what potential instabilities may occur given certain configurations of the magnetic field. In particular, a purely magnetic instability can occur…
The nonlinear evolution of Alfv\'enic fluctuations in the firehose unstable regime is investigated numerically and theoretically for an anisotropic plasma described by the one-fluid double adiabatic equations. We revisit the traditional…
We investigate the stability and instability of the magnetic Rayleigh--B\'enard problem with zero resistivity. An stability criterion is established, under which the magnetic B\'enard problem is stable. The proof mainly is based on a…
We consider the dynamics of two layers of incompressible electrically conducting fluid interacting with the magnetic field, which are confined within a 3D horizontally infinite slab and separated by a free internal interface. We assume that…
Electromagnetic field configurations with vanishing Lorentz force density are known as force-free and appear in terrestrial, space, and astrophysical plasmas. We explore a general method for finding such configurations based on formulating…
We study the 3D magnetohydrodynamics (MHD) equations in an annular cylinder, perturbed around the explicit steady state given by the 3D Taylor-Couette velocity field and zero magnetic field. Combining a recent linear instability result for…
We perform numerical simulations of nonlinear MHD waves in a gravitationally stratified molecular cloud that is bounded by a hot and tenuous external medium. We study the relation between the strength of the turbulence and various global…
Transverse quasilinear relaxation of the cyclotron-Cherenkov instability in the inhomogeneous magnetic field of pulsar magnetospheres is considered. We find quasilinear states in which the kinetic cyclotron-Cherenkov instability of a beam…
A shared property of several of the known exact solutions to the equations of force-free electrodynamics is that their charge-current four-vector is \textit{null}. We examine the general properties of null-current solutions and then focus…
The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such…
We investigate the nonlinear instability of a smooth Rayleigh-Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible nonhomogeneous magnetohydrodynamic (MHD)…
The Casimir force for charge-neutral, perfect conductors of non-planar geometric configurations have been investigated. The configurations are: (1) the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical shell. The…
We prove the existence of diffusing solutions in the motion of a charged particle in the presence of an ABC magnetic field. The equations of motion are modeled by a 3DOF Hamiltonian system depending on two parameters. For small values of…
In this paper, we solve a long-standing open problem: nonlinear stability of current-vortex sheet in the ideal incompressible Magneto-Hydrodynamics under the linear stability condition. This result gives a first rigorous confirmation of the…
In previous works [4, 5], existence and uniqueness of travelling waves for the nonlinear Schr\"odinger equations have been shown for speeds close to the speed of sound. Furthermore, it has been proved that a chain of dark solitons of…