Related papers: Blowup for the forced electron MHD
Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria. Within a physically simplified, but exact…
We address the compressible magnetohydrodynamics (MHD) equations in $\mathbb{R}^3$ and establish a blow-up criterion for the local strong solutions in terms of the density only. Namely, if the density is away from vacuum ($\rho= 0$) and the…
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…
Extended magnetohydrodynamics (XMHD) is a fluid plasma model generalizing ideal MHD by taking into account the impact of Hall drift effects and the influence of electron inertial effects. XMHD has a Hamiltonian structure which has received…
We investigate a role of the Hall-effect in the current sheet evolution and onset of the secondary tearing (plasmoid) instability in the framework of the incompressible resistive Hall-magnetohydrodynamics (MHD). The model under…
Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the…
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 examine the range of rest-mass densities, temperatures and magnetic fields involved in simulations of binary neutron star mergers (BNSM) and identify the conditions under which the ideal magneto-hydrodynamics (MHD) breaks down using…
Parker problem in Hall magnetohydrodynamics (MHD) is considered. Poloidal shear into the toroidal flow generated by the Hall effect is incorporated. This is found to lead to a {\it triple deck} structure for the Parker problem in Hall MHD,…
We consider the electron magnetohydrodynamics (MHD) equation on the 3D torus $\mathbb T^3$. For a given smooth vector field $H$ with zero mean and zero divergence, we can construct a weak solution $B$ to the electron MHD in the space…
Hall instability in electron magnetohydrodynamics is interpreted as the shear-Hall instability driven jointly by helicoidal oscillations and shear in the electron current velocity. This explanation suggests an antiparallel orientation of…
The aim of this paper is to study, in dimensions 2 and 3, the pure-power non-linear Schr\"odinger equation with an external uniform magnetic field included. In particular, we derive a general criteria on the initial data and the power of…
It has been shown that in metals and semiconductors the joint action of permanent magnetic and AC electric fields leads to arising of DC surface electric current. This is due to essentially non-linear dynamics of electronic gas in surface…
In this paper we investigate the dynamics of magnetic helicity in magnetohydrodynamic (MHD) turbulent flows focusing at scales larger than the forcing scale. Our results show a nonlocal inverse cascade of magnetic helicity, which occurs…
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.…
In this work we extend the non-ideal magnetohydrodynamics (MHD) solver in the moving mesh code AREPO to include the Hall effect. The core of our algorithm is based on an estimation of the magnetic field gradients by a least-square…
Anisotropy of kinetic coefficients in presence of a magnetic field is represented by Hall currents, which appear in a collisional medium due to action of the Lorentz force on the charged particles between collisions. We derive equations,…
We give sufficient conditions on the initial data so that a semilinear wave inequality blows-up in finite time. Our method is based on the study of an associated second order differential inequality. The same method is applied to some…
According to magnetohydrodynamics (MHD), the encounter of two collisional magnetized plasmas at high velocity gives rise to shock waves. Investigations conducted so far have found that the same conclusion still holds in the case of…
This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup…