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Hydrodynamics of plasma in the random magnetic field is considered, which is characterized by the second moment of magnetic induction. Equations of ideal magnetic hydrodynamics in such field are received for an adiabatic process. It is…
In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the…
The numerical solution of the Milne problem for semi-infinite plane-parallel magnetized electron atmosphere is obtained. It is assumed that magnetic field is directed along the normal to the atmosphere. The angular dependence, the…
The planets magnetic field has been explained based on the dynamo theory, which presents as many difficulties in mathematical terms as well as in predictions. It proves to be extremely difficult to calculate the dipolar magnetic moment of…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
In this paper we obtain an exact periodic solution for the system of equations of state corresponding to the spiral phase of crystalline ordering. We used method of integral rational basis of invariants to construct an inhomogeneous Landau…
In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field…
Active regions (ARs) are typical magnetic structures found in the solar atmosphere. We calculate several magnetohydrostatic (MHS) equilibrium models that include the effect of a finite plasma-$\beta$ and gravity and that are representative…
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects…
It is shown that transonic plasma acceleration in the converging-diverging magnetic field (magnetic nozzle) follows the unique global solution which is fully defined by the magnetic field. Such solution, which was analytically obtained…
The equations governing the magnetohydrodynamic stagnation point flow toward a non-conducting, thermally insulated, nonporous, linearly stretching sheet are cast in a self similar form. Consistent boundary conditions on the velocity,…
An oblique pulsar magnetosphere with a plasma conductivity is studied by using a pseudo-spectral method. In the pseudo-spectral method, the time-dependent Maxwell equations are solved, both electric and magnetic fields are expanded in terms…
In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…
The non-collisional interaction between conducting obstacles and magnetized plasma winds can be found in different scenarios, from the interaction occurring between regions inside galaxy clusters to the interaction between the solar wind…
In this paper we exclude the scenario of apparition of finite time singularity in the form of self-similar singularities in the ideal magnetohydrodynamic equations, assuming suitable integrability conditions on the vorticity and the…
The dynamical coupling between the solar chromospheric plasma and magnetic field is investigated by numerically solving a fully self-consistent, two-dimensional initial-value problem for the nonlinear collisional MHD equations including…
This paper is concerned with the asymptotic behaviors of global strong solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in two-dimensional periodic domains in…
In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are derived from the two dimensional density-dependent incompressible MHD equations.Under…
We resolve the paradox that although magnetic collimation of an isotropic solar wind results in an enhancement of its proton flux along the polar directions, several observations indicate a wind proton flux peaked at the equator. To that…
We consider the free boundary problem for a plasma--vacuum interface in ideal incompressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic field obeys the div-curl system of pre-Maxwell dynamics, we do not…