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

doi:10.1007/s10473-021-0410-z

Abstract

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

CLC Number:

35Q35

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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