Singular limit for the magnetohydrodynamics of the damped wave type in the critical Fourier–Sobolev space

Global existence and uniqueness of the 2D damped wave-type MHD equations

“…In recent years the global regularity issue of the magnetohydrodynamic equations has attracted considerable interests and much important progress has been made (see, e.g., [1,2,4,[6][7][8][9]). In the case when α = β = 1, (1.1) becomes the standard MHD-wave equations, which can be formally derived from the coupled Maxwell-Ohm equations, we refer to [3,5] for details. Very recently, the small data global well-posedness and a singular limit of the problem in Fourier-Sobolev spaces have been obtained [5].…”

“…In the case when α = β = 1, (1.1) becomes the standard MHD-wave equations, which can be formally derived from the coupled Maxwell-Ohm equations, we refer to [3,5] for details. Very recently, the small data global well-posedness and a singular limit of the problem in Fourier-Sobolev spaces have been obtained [5]. Based on the global well-posedness results of the two-dimensional magnetohydrodynamic equations, Ji-Wu-Xu [3] proved the global wellposedness for the standard MHD-wave equations when γ and the size of the initial data satisfy a suitable constraint.…”