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<p>This paper aims to understand the role of the small relaxation time and retardation time on the hydrostatic approximation of viscoelastic fluids. The goal of this paper is twofold. Firstly, we derive the asymptotic limit of the three-dimensional Oldroyd-B model in a thin strip, when the relaxation time, retardation time and dynamical viscosity proportionally converge to 0. Secondly, we address the global well-posedness of the derived system with small analytic initial data.</p>

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On the hydrostatic approximation of viscoelastic fluids with small relaxation and retardation time

  • 期刊论文

  • 发表日期：

    2026年5月11日

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  • Marius Paicu,
  • Tianyuan Yu,
  • Ning Zhu

摘要

This paper aims to understand the role of the small relaxation time and retardation time on the hydrostatic approximation of viscoelastic fluids. The goal of this paper is twofold. Firstly, we derive the asymptotic limit of the three-dimensional Oldroyd-B model in a thin strip, when the relaxation time, retardation time and dynamical viscosity proportionally converge to 0. Secondly, we address the global well-posedness of the derived system with small analytic initial data.