The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant...

Abstract Special features of magnetohydrodynamic waves linear dynamics in smooth shear flows are studied. Quantitative asymptotic and numerical analysis are performed for wide range of system parameters when basic flow has constant shear of velocity and uniform magnetic field is parallel to the basic flow. The special features consist of magnetohydrodynamic wave mutual transformation and over-r...

We study the connection between the long-time dynamics of the 3D magnetohydrodynamicα model and the exact 3D magnetohydrodynamic system. We prove that the trajectory attractor Uα of the 3D magnetohydrodynamic-α model converges to the trajectory attractor U0 of the 3D magnetohydrodynamic system (in an appropriate topology) when α approaches zero.

The discovery of magnetohydrodynamic waves was a major breakthrough in plasma physics and its applications to space physics and fusion research. The waves were discovered by Hannes Alfvén and are therefore also called Alfvén Waves. The discovery was typical of Alfvén’s outstanding ability to derive results of great generality from analysis of specific problems—in this case, the sunspots and the...

In this paper we establish the local exact internal controllability for the two-dimensional magnetohydrodynamic equations. The needed Carleman estimate for the adjoint linearized magnetohydrodynamic equations is also obtained here.

Abstract. The compactness of weak solutions to the magnetohydrodynamic equations for the viscous, compressible, heat conducting fluids is considered in both the three-dimensional space R and the three-dimensional periodic domains. The viscosities, the heat conductivity as well as the magnetic coefficient are allowed to depend on the density, and may vanish on the vacuum. This paper provides a d...

Abstract. We study the exact controllability for the magnetohydrodynamic equations in multi-connected bounded domains. We show that the value of any solution of the magnetohydrodynamic system at any given time is locally exactly controllable provided that this solution is smooth enough. This means that the chosen value of such a solution can be reached by starting from initial states which are ...

This paper studies the three-dimensional density-dependent incompressible magnetohydrodynamic equations. First, a regularity criterion is proved which allows the initial density to contain vacuum. Then we establish another blow-up criterion in the Besov space Ḃ0 ∞,2 when the positive initial density is bounded away from zero. Third, we prove a global nonexistence result for initial density with...

The dynamics of spectral transport in two-dimensional turbulent convection of electrically conducting fluids is studied by means of direct numerical simulations in the frame of the magnetohydrodynamic Boussinesq approximation. The system performs quasioscillations between two different regimes of small-scale turbulence: one dominated by nonlinear magnetohydrodynamic interactions; the other gove...

Abstract. This paper is concerned with the combined incompressible and inviscid limit of the compressible magnetohydrodynamic equations in the whole space with general initial data. It is rigorously showed that, as the Mach number, the shear viscosity coefficient and the magnetic diffusion coefficient simultaneously go to zero, the weak solution of the compressible magnetohydrodynamic equations...