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Large-Time Behavior of Solutions to the Inflow Problem of the Non-Isentropic Micropolar Fluid Model

Authors
  • Gao, Junpei1
  • Cui, Haibo1
  • 1 Huaqiao University, Quanzhou, 362021, China , Quanzhou (China)
Type
Published Article
Journal
Acta Mathematica Scientia
Publisher
Springer-Verlag
Publication Date
Jun 01, 2021
Volume
41
Issue
4
Pages
1169–1195
Identifiers
DOI: 10.1007/s10473-021-0410-z
Source
Springer Nature
Keywords
License
Yellow

Abstract

We investigate the asymptotic behavior of solutions to the initial boundary value problem for the micropolar fluid model in a half line ℝ+ ≔ (0, ∞). 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.

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