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Rigorous derivation of incompressible e-MHD equations from compressible Euler-Maxwell equations. (English) Zbl 1170.35081
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.

MSC:
35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
76W05 Magnetohydrodynamics and electrohydrodynamics
35C20 Asymptotic expansions of solutions to PDEs
35L60 First-order nonlinear hyperbolic equations
35B45 A priori estimates in context of PDEs
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