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<p>This paper investigates the free interface problem of incompressible Navier–Stokes–Darcy equations in a three-dimensional finite-depth domain. The domain is divided into two distinct subsets by a freely moving interface. We establish the global well-posedness of Navier–Stokes–Darcy equations in low regularity Sobolev spaces. Additionally, we demonstrate that the solution decays at an exponential rate.</p>

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Low regularity well-posedness for the Navier–Stokes–Darcy equations with free interface

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Ningning Gao,
  • Qimeng Yang,
  • Lei Yao

摘要

This paper investigates the free interface problem of incompressible Navier–Stokes–Darcy equations in a three-dimensional finite-depth domain. The domain is divided into two distinct subsets by a freely moving interface. We establish the global well-posedness of Navier–Stokes–Darcy equations in low regularity Sobolev spaces. Additionally, we demonstrate that the solution decays at an exponential rate.