Convergence and non-convergence phenomena in Euler-Maxwell to MHD transitions

2025/04/26 by Dong-ha Kim, Junha Kim, Kim, Dong-ha +3
Mathematics · #35Q35 #35Q60 #76D03 #76W05 #78A25 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Convergence (economics) #Current (fluid) #Electric current #Electric field #FOS: Mathematics #Flow (mathematics) #Infinity #Magnetic field #Magnetohydrodynamics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2504.18890

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2025/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD system, auxiliary linear system and error part system. As a result, we obtain the convergence of the velocity of the fluid u, electric fields E and magnetic fields B from the Euler-Maxwell system toward the MHD system in L^p_tL²_x as the speed of light c approaches infinity for p∈[1,∞]. We also derived non-convergence results of electric current j or cE, and these results are classified by a certain threshold for p. Finally, we investigate how the L²-energy flow of Euler-Maxwell system evolves as c tends to infinity, leading to the vanishing of Ampère's equation in the Euler-Maxwell system.

Citations

• Global unique solutions to the planar inhomogeneous Navier--Stokes--Maxwell equations
• Stability analysis of two-dimensional ideal flows with applications to viscous fluids and plasmas
• Damped Strichartz estimates and the incompressible Euler--Maxwell system
• Solutions of Navier--Stokes--Maxwell systems in large energy spaces
• From the Vlasov-Maxwell-Boltzmann system to incompressible viscous electro-magneto-hydrodynamics
• Well-posedness for Hall-magnetohydrodynamics
• Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data

Related

• Convergence of the Schrödinger-Poisson system to the Euler equations under the influence of a large magnetic field
• On convergence of numerical solutions for the compressible MHD system with weakly divergence-free magnetic field
• Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain
• The incompressible limit of the Euler-Maxwell two-fluid system
• Darcy's law and diffusion for a two-fluid Euler-Maxwell system with dissipation