On the Cauchy problem of compressible Micropolar fluids subjected to Hall current

Mingyu Zhang; Mingyu Zhang

doi:10.3934/math.20241627

AIMS Mathematics

2024, Volume 9, Issue 12: 34147-34183. doi: 10.3934/math.20241627

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Research article

On the Cauchy problem of compressible Micropolar fluids subjected to Hall current

Mingyu Zhang ^,

School of Mathematics and Statistics, Weifang University, Weifang 261061, China

Received: 17 October 2024 Revised: 24 November 2024 Accepted: 28 November 2024 Published: 04 December 2024
MSC : 35A01, 35Q35, 76W05

In this paper, the large-time behavior of global strong solutions is justified for the three dimensional compressible micropolar fluids subjected to Hall current. Both the global existence and the optimal decay rates of strong solutions are obtained when the smooth initial data are sufficiently close to the non-vacuum equilibrium in $ H^1 $. In addition, the vanishing limit of the Hall coefficient is also justified.
- micropolar fluids,
- Hall current,
- optimal decay rates,
- vanishing Hall limit
Citation: Mingyu Zhang. On the Cauchy problem of compressible Micropolar fluids subjected to Hall current[J]. AIMS Mathematics, 2024, 9(12): 34147-34183. doi: 10.3934/math.20241627

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Abstract

In this paper, the large-time behavior of global strong solutions is justified for the three dimensional compressible micropolar fluids subjected to Hall current. Both the global existence and the optimal decay rates of strong solutions are obtained when the smooth initial data are sufficiently close to the non-vacuum equilibrium in $ H^1 $. In addition, the vanishing limit of the Hall coefficient is also justified.

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