Abstract
This paper studies the asymptotic limit for solutions to the equations of magnetohydrodynamics, specifically, the Navier–Stokes–Fourier system describing the evolution of a compressible, viscous, and heat conducting fluid coupled with the Maxwell equations governing the behavior of the magnetic field, when Mach number and Alfven number tends to zero. The introduced system is considered on a bounded spatial domain in $${\mathbb{R}^{3}}$$ , supplemented with conservative boundary conditions. Convergence towards the incompressible system of the equations of magnetohydrodynamics is shown.
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