TY - JOUR
T1 - Singular limit for the magnetohydrodynamics of the damped wave type in the critical Fourier–Sobolev space
AU - Matsui, Tatsuya
AU - Nakasato, Ryosuke
AU - Ogawa, Takayoshi
N1 - Funding Information:
R. Nakasato is supported by Grant-in-Aid for JSPS Fellows JP19J11320 . T. Ogawa is supported by JSPS Grant in aid for Scientific Research (S) JP19H05597 and Challenging Research (Pioneering) JP20K20284 .
Publisher Copyright:
© 2020 The Authors
PY - 2021/1/15
Y1 - 2021/1/15
N2 - 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.
AB - 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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U2 - 10.1016/j.jde.2020.08.023
DO - 10.1016/j.jde.2020.08.023
M3 - Article
AN - SCOPUS:85091097928
SN - 0022-0396
VL - 271
SP - 414
EP - 446
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -