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

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

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 th...

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Bibliographic Details
Published in:Journal of Differential Equations Vol. 271; pp. 414 - 446
Main Authors: Matsui, Tatsuya, Nakasato, Ryosuke, Ogawa, Takayoshi
Format: Journal Article
Language:English
Published: Elsevier Inc 15-01-2021
Online Access:Get full text
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Summary: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.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2020.08.023