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

Abstract

We study the Cauchy problem of the incompressible damped wave type magnetohydrodynamic system in RN (N≥2). The purpose of this paper is to show the global well-posedness and a singular limit of the problem in Fourier–Sobolev spaces. For the proof of the results, we use the Lp-Lq type estimates for the fundamental solutions of the damped wave equation and end-point maximal regularity for the inhomogeneous heat equation in that space with a detailed estimate of difference between the symbol of the heat kernel and fundamental solution of the damped wave equation.

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