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<p>In this paper, we focus on a two-dimensional (2D) complex fluid model in a slab domain. Based on time-weighted energy estimates, we work in Eulerian coordinates to establish the stability and algebraical decay-in-time behavior near hydrostatic equilibrium of the 2D complex fluid model with Navier(-slip) boundary condition. Since the 2D complex fluid model can be obtained from the equations of 2D incompressible nonresistive magnetohydrodynamic (MHD) fluids by a transformation of the stream function, as a byproduct, we also obtain the stability and the algebraical decay-in-time behavior of the 2D incompressible nonresistive MHD equations with an impressed horizontal magnetic field in a slab domain. Our results enrich the small perturbation theory in both the complex fluid model in (Lin and Zhang in Arch. Ration. Mech. Anal. 216: 905–920, <CitationRef CitationID="CR15">2015</CitationRef>) and the nonresistive MHD equations in (Ren et al. in Nonlinearity 29:1257, <CitationRef CitationID="CR20">2016</CitationRef>).</p>

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Stability of the two-dimensional complex fluid model in a slab domain

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月15日

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  • Chengrong Zhang,
  • Yajie Zhang

摘要

In this paper, we focus on a two-dimensional (2D) complex fluid model in a slab domain. Based on time-weighted energy estimates, we work in Eulerian coordinates to establish the stability and algebraical decay-in-time behavior near hydrostatic equilibrium of the 2D complex fluid model with Navier(-slip) boundary condition. Since the 2D complex fluid model can be obtained from the equations of 2D incompressible nonresistive magnetohydrodynamic (MHD) fluids by a transformation of the stream function, as a byproduct, we also obtain the stability and the algebraical decay-in-time behavior of the 2D incompressible nonresistive MHD equations with an impressed horizontal magnetic field in a slab domain. Our results enrich the small perturbation theory in both the complex fluid model in (Lin and Zhang in Arch. Ration. Mech. Anal. 216: 905–920, 2015) and the nonresistive MHD equations in (Ren et al. in Nonlinearity 29:1257, 2016).