The velocity-current formulation of magnetohydrodynamics

Generalized entropy formulation of dissipative magnetohydrodynamics.

A variational-principle formulation of dissipative magnetohydrodynamics (DMHD) including thermal conduction and viscous dissipation as well as resistive decay is presented. The functional to be minimized is an extension of the generalized entropy-production (GEP) rate first discussed by I. Prigogine [Nonequilibrium Thermodynamics, Variationa! Techniques, and Stability, edited by R. J. Donnelly,...

Noncanonical Hamiltonian Density Formulation of Hydrodynamics and Ideal Magnetohydrodynamics

ity a nonlocal potential which could fit neutron elastic scattering data in the energy range from 0.4 to 24 MeV and where the optical-model parameters were energy independent. This is, of course, a remarkable result since we know that the absorption, for instance, is changing quite dramatically by going from 0.4 to 24 MeV incident projectile energy. We believe that these findings of Perey and B...

PUBLISHED VERSION Potential Vorticity Formulation of Compressible Magnetohydrodynamics

A Practical Optimal Control Approach to the Stationary Mhd System in Velocity–current Formulation

An optimal control problem for the equations governing the stationary problem of magnetohydrodynamics (MHD) is considered. Control mechanisms by external and injected currents and magnetic fields are treated. Motivated by practical applications, an optimal control problem is formulated. First order necessary and second order sufficient conditions are developed. An operator splitting scheme for ...

On the localization of the magnetic and the velocity elds in the equations of magnetohydrodynamics

We study the behavior at in nity, with respect to the space variable, of solutions to the magnetohydrodynamics equations in Rd. We prove that if the initial magnetic eld decays su ciently fast, then the plasma ow behaves as a solution of the free nonstationnary Navier Stokes equations when |x| → +∞, and that the magnetic eld will govern the decay of the plasma, if it is poorly localized at the ...