Magnetohydrodynamics approximation of the compressible full magneto- micropolar system

Jishan Fan; Tohru Ozawa; Jishan Fan; Tohru Ozawa

doi:10.3934/math.2022878

AIMS Mathematics

2022, Volume 7, Issue 9: 16037-16053. doi: 10.3934/math.2022878

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Research article

Magnetohydrodynamics approximation of the compressible full magneto- micropolar system

Jishan Fan ¹,
Tohru Ozawa ^{2
,
,}

1.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

Received: 23 May 2022 Revised: 14 June 2022 Accepted: 20 June 2022 Published: 30 June 2022
MSC : 35B25, 35Q60, 76W05

In this paper, we will use the Banach fixed point theorem to prove the uniform-in-$ \epsilon $ existence of the compressible full magneto-micropolar system in a bounded smooth domain, where $ \epsilon $ is the dielectric constant. Consequently, the limit as $ \epsilon\rightarrow0 $ can be established. This approximation is usually referred to as the magnetohydrodynamics approximation and is equivalent to the neglect of the displacement current.
- magneto micropolar,
- uniform existence,
- dielectric constant
Citation: Jishan Fan, Tohru Ozawa. Magnetohydrodynamics approximation of the compressible full magneto- micropolar system[J]. AIMS Mathematics, 2022, 7(9): 16037-16053. doi: 10.3934/math.2022878

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Abstract

In this paper, we will use the Banach fixed point theorem to prove the uniform-in-$ \epsilon $ existence of the compressible full magneto-micropolar system in a bounded smooth domain, where $ \epsilon $ is the dielectric constant. Consequently, the limit as $ \epsilon\rightarrow0 $ can be established. This approximation is usually referred to as the magnetohydrodynamics approximation and is equivalent to the neglect of the displacement current.

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