Existence theorems for two-fluid magnetohydrodynamics

The description of a plasma as composed by two types of fluids, formed by ions and electrons, is more complete than the classical one-fluid magnetohydrodynamics (MHD) model and it has proved necessary to explain the phenomena of fast magnetic reconnection. We prove a finite-time theorem of existence and uniqueness of solutions for this system for either Dirichlet or periodic boundary conditions in dimension three. It turns out that the regularity estimates for the magnetic field are finer than the MHD ones.