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

초록

In this work, we investigate the difference estimate for a class of Euler–Maxwell systems 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 fluid velocity u, electric field E and magnetic field B from the Euler–Maxwell system toward the MHD system in mixed-norm spaces LtpLx2 as the speed of light c approaches infinity for p∈[1,∞]. We also derive 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 term in the Euler–Maxwell system.

키워드