Related papers: No unique solution to the seismological problem of…
Magnetohydrodynamic (MHD) wave activity is ubiquitous in the solar atmosphere. MHD seismology aims to determine difficult to measure physical parameters in solar atmospheric magnetic and plasma structures by a combination of observed and…
The minimalist approach in the study of perturbations in fluid dynamics and magnetohydrodynamics involves describing their evolution in the linear regime using a single first-order ordinary differential equation, dubbed principal equation.…
Magnetic twist is thought to play an important role in coronal loops. The effects of magnetic twist on stable magnetohydrodynamic (MHD) waves is poorly understood because they are seldom studied for relevant cases. The goal of this work is…
We investigate standing kink magnetohydrodynamic (MHD) oscillations in a prominence fine structure modeled as a straight and cylindrical magnetic tube only partially filled with the prominence material, and with its ends fixed at two rigid…
The aim is to justify rigorously the so-called reduced magnetohydrodynamic model (abbreviated as RMHD), which is widely used in fusion, space and astrophysical plasmas. Motivated by physics, the focus is on plasmas that are simultaneously…
We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic…
Periodic waves of the modified Korteweg-de Vries (mKdV) equation are identified in the context of a new variational problem with two constraints. The advantage of this variational problem is that its non-degenerate local minimizers are…
We investigate the propagation of MHD waves in a homogenous, magnetized plasma in a weakly stratified atmosphere, representing hot coronal loops. In most of earlier studies a time-independent equilibrium is considered. Here we abandon this…
In the past few years observations by high-resolution space imaging telescopes and spectrometers have confirmed that a great variety of MHD waves are supported in the solar corona of a low-beta plasma and fine structure. MHD waves are an…
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…
We present a method to assess the plausibility of alternative mechanisms to explain the damping of magnetohydrodynamic (MHD) transverse waves in solar coronal loops. The considered mechanisms are resonant absorption of kink waves in the…
This article proposes a review of the analysis of the system of magnetohydrodynamics (MHD). First, we give an account of the modelling asumptions. Then, the results of existence of weak solutions, using the notion of renormalized solutions.…
Context. Kink waves are routinely observed in coronal loops. Resonant absorption is a well-accepted mechanism that extracts energy from kink waves. Nonlinear kink waves are know to be affected by the Kelvin-Helmholtz instability. However,…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
The theory of magnetohydrodynamic (MHD) waves in solar coronal slabs in a zero-$\beta$ configuration and for parallel propagation of waves does not allow the existence of surface waves. When oblique propagation of perturbations is…
Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in…
Kink magnetohydrodynamic (MHD) waves are frequently observed in various magnetic structures of the solar atmosphere. They may contribute significantly to coronal heating and could be used as a tool to diagnose the solar plasma. In this…
Observations of transversal coronal loop oscillations very often show the excitation and damping of oscillations in groups of coronal loops rather than in individual and isolated structures. We present results on the oscillatory properties…
Magnetoacoustic oscillations are nowadays routinely observed in various regions of the solar corona. This allows them to be used as means of diagnosing plasma parameters and processes occurring in it. Plasma diagnostics, in turn, requires a…
Magnetohydrodynamics in divergence form describes a hyperbolic system of covariant and constraint-free equations. It comprises a linear combination of an algebraic constraint and Faraday's equations. Here, we study the problem of…