Uniform existence of the 1-d complete equations for an electromagnetic fluid

In this paper, we prove the global-in-time and uniform-in-ϵ existence of the 1-d complete equations for an electromagnetic fluid in a bounded interval without vacuum, where ϵ is the dielectric constant. Consequently, the limit as ϵ → 0 can be established. This approximation is usually referred to as the magnetohydrodynamic approximation, and is equivalent to the neglect of the displacement current.