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

2021/03/15 by Lin Ma, Boling Guo, Ma, Lin +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2103.08344

openalex publication_date 2021/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Novotný et al. and Vasseur et al. For academic~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 preposed hypotheses and remove some unnecessary conditions of the main theorem in Novotný et al. Meanwhile, the same proof method can be used for real~magnetic~bi-fluid~system combined with pressure law proposed in Vasseur et al.

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