Global weak solutions to some two-fluid models with magnetic field

Abstract

We prove the existence of global weak solutions with finite energy to some two-fluid systems with magnetic field and the results suit for corresponding two-fluid systems. The proof method is mainly inspired by Novotn\'y et al. and Vasseur et al. For $academic~magnetic~ bi\text{-}fluid~ system$, we focus on the case of pressure law with ideal gases and the new ingredient is that we can make the proof more explicit without using the preposed hypotheses and remove some unnecessary conditions of the main theorem in Novotn\'y et al. Meanwhile, the same proof method can be used for $real~magnetic~bi\text{-}fluid~system$ combined with pressure law proposed in Vasseur et al.