LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL

doi:10.1007/s10473-021-0410-z

数学物理学报(英文版) ›› 2021, Vol. 41 ›› Issue (4): 1169-1195.doi: 10.1007/s10473-021-0410-z

LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL

高俊培, 崔海波

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

收稿日期:2020-03-07 修回日期:2020-10-26 出版日期:2021-08-25 发布日期:2021-09-01
通讯作者: Haibo CUI E-mail:hbcui@hqu.edu.cn
基金资助:
The research was supported by the National Natural Science Foundation of China (11601164, 11971183), the Fundamental Research Funds for the Central Universities (ZQN-701) and the Natural Science Foundation of Fujian Province of China (2020J01071).

LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL

Junpei GAO, Haibo CUI

School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

Received:2020-03-07 Revised:2020-10-26 Online:2021-08-25 Published:2021-09-01
Contact: Haibo CUI E-mail:hbcui@hqu.edu.cn
Supported by:
The research was supported by the National Natural Science Foundation of China (11601164, 11971183), the Fundamental Research Funds for the Central Universities (ZQN-701) and the Natural Science Foundation of Fujian Province of China (2020J01071).

摘要/Abstract

摘要： We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line $\mathbb{R}_{+}:=(0,\infty).$ Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotically stable under some smallness conditions. Meanwhile, we obtain the global existence of solutions based on the basic energy method.

关键词: Micropolar fluid model, composite wave, inflow problem, stability

Abstract: We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line $\mathbb{R}_{+}:=(0,\infty).$ Inspired by the relationship between a micropolar fluid model and Navier-Stokes equations, we prove that the composite wave consisting of the transonic boundary layer solution, the 1-rarefaction wave, the viscous 2-contact wave and the 3-rarefaction wave for the inflow problem on the micropolar fluid model is time-asymptotically stable under some smallness conditions. Meanwhile, we obtain the global existence of solutions based on the basic energy method.

Key words: Micropolar fluid model, composite wave, inflow problem, stability

中图分类号:

35Q35

高俊培, 崔海波. LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL[J]. 数学物理学报(英文版), 2021, 41(4): 1169-1195.

Junpei GAO, Haibo CUI. LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL[J]. Acta mathematica scientia,Series B, 2021, 41(4): 1169-1195.

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LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL

LARGE-TIME BEHAVIOR OF SOLUTIONS TO THE INFLOW PROBLEM OF THE NON-ISENTROPIC MICROPOLAR FLUID MODEL

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