an:05534313
Zbl 1170.35081
Peng, Yue-Jun; Wang, Shu
Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations
EN
SIAM J. Math. Anal. 40, No. 2, 540-565 (2008).
00247577
2008
j
35Q35 35B40 76W05 35C20 35L60 35B45
Euler-Maxwell equations; incompressible electron magnetohydrodynamics equations; quasi-neutral limit; weighted energy
The incompressible e-MHD equations from compressible Euler-Maxwell equations are derived via the quasi-neutral regime. Assuming that the initial data are well prepared for the electric density, electric velocity, and magnetic field (but not necessarily for the electric field), the convergence of the smooth solutions of the compressible Euler-Maxwell equations in a torus to the solutions of the incompressible e-MHD equations (on time intervals on which a smooth solution of the incompressible e-MHD exists) is proved rigorously by using weighted energy technique. One of the main tools for establishing uniform a priori estimates is the use of the curl-div decomposition of the gradient and the wave-type equation of the Maxwell equations.
Titus Petrila (Cluj-Napoca)