Scholarlink

<p>This paper provides the first study of the homogenization of the 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of supercritical size. The diameter of the holes is of order <i>ε</i><sup><i>α</i></sup> (1 &lt; <i>α</i> &lt; 3), where <i>ε</i> &gt; 0 is a small parameter measuring the mutual distance between the holes. We show that as <i>ε</i> → 0, the asymptotic limit behavior of velocity and density is governed by Darcy’s law under the assumption of a strong solution of the limiting system. Moreover, convergence rates are obtained. Finally, we show the existence of strong solutions to the inhomogeneous incompressible Darcy law, which might be of independent interest.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Qualitative derivation of a density-dependent incompressible Darcy law

  • 期刊论文

  • 发表日期：

    2026年5月22日

查看全文
  • Danica Basarić,
  • Florian Oschmann,
  • Jiaojiao Pan

摘要

This paper provides the first study of the homogenization of the 3D non-homogeneous incompressible Navier-Stokes system in perforated domains with holes of supercritical size. The diameter of the holes is of order εα (1 < α < 3), where ε > 0 is a small parameter measuring the mutual distance between the holes. We show that as ε → 0, the asymptotic limit behavior of velocity and density is governed by Darcy’s law under the assumption of a strong solution of the limiting system. Moreover, convergence rates are obtained. Finally, we show the existence of strong solutions to the inhomogeneous incompressible Darcy law, which might be of independent interest.