Work

Hall–MHD System as a Simplified One-Fluid Ion Model Derived from Two-Fluid Euler–Maxwell Equations

Year: 2026

Type: article

Abstract: . We derive the one-fluid ion model from the partial-compressible two-fluid Euler–Maxwell system with a collision mechanism in which the ions are considered compressible while electrons are not. Deriving such a model based solely on the zero-electron-mass limit or the quasi-neutral limit is quite open because of the singularities of the electric field and the strong coupling effects of the Lorentz forces. In this work, we apply the combined zero-electron-mass and quasi-neutral limit. We prove the global-in-time existence and the combined limit of smooth solutions. Furthermore, for well-prepared initial data, we establish the error estimates of the convergence between smooth solutions to one-fluid and two-fluid models. It is worth mentioning that the velocities of ions and electrons are different in this study.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/25m1733033

Authors: Yue-Jun Peng, Shuai Xi, Liang Zhao

Institutions: Centre National de la Recherche Scientifique, Université Clermont Auvergne, Laboratoire de Mathématiques Blaise Pascal, Shandong University of Science and Technology, National University of Singapore

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Natural Science Foundation of Shandong Province

Awards: G7680904739, G7986811962