Motion of an incompressible conducting liquid in a strong self-consistent magnetic field (Q1180267)

In the present paper, the approach to the analysis of the self-consistent magnetohydrodynamic problem is extended to the case of an incompressible liquid with finite conductivity. A study is made of the closed reduced system of \(MHD\) equations obtained from the complete model in the zeroth order in the small parameter \(A^{-1}\), in which the magnetic field is a force-free field. An investigation is made of the free diffusion of a force-free magnetic field with constant coefficient \(\alpha\) of proportionality between the current density and the magnetic induction in a spatially unbounded liquid, and the kinematic properties of a velocity field of the liquid in which the force-free nature of the magnetic field is maintained during the damping process are determined. It is shown that the complete class of such velocity fields is represented by the group of rigid-body motions of the liquid.