Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations

Abstract

The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic approximation in physical books. In this paper we justify this singular limit rigorously in the framework of smooth solutions for well-prepared initial data.