Global Weak Solution to Real Bi-Fluid System with Magnetic Field

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 Novotný et al. [10] and Vasseur et al. [12]. For real magnetic bi-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 proposed hypotheses and remove some unnecessary conditions of the main theorem in Novotný et al. [10]. Meanwhile, the same proof method works for academic magnetic bi-fluid system with pressure law proposed in Vasseur et al. [12].