Abstract We study the Cauchy problem of the incompressible damped wave type magnetohydrodynamic system in R N ( 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 L p - L q 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.

中文翻译：

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临界傅里叶-索博列夫空间中阻尼波型磁流体动力学的奇异极限

摘要 研究了RN(N≥2)中不可压缩阻尼波型磁流体动力系统的柯西问题。本文的目的是展示傅里叶-索博列夫空间中问题的全局适定性和奇异极限。为了证明结果，我们对阻尼波动方程的基本解使用 L p - L q 类型估计，并使用该空间中非均匀热方程的端点最大正则性，并详细估计了符号之间的差异阻尼波动方程的热核和基本解。