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<p>In this paper, we study the homogenization of 3<i>D</i> non-homogeneous incompressible Navier–Stokes system in perforated domains with holes of critical size. Under very mild assumptions concerning the shape of the obstacles and their mutual distance, we show that when <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="21_2025_931_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \rightarrow 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, the velocity and density converge to a solution of the non-homogeneous incompressible Navier–Stokes system with a friction term of Brinkman type.</p>

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Homogenization of Non-Homogeneous Incompressible Navier–Stokes System in Critically Perforated Domains

  • 期刊论文

  • 发表日期：

    2025年3月4日

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  • Jiaojiao Pan

摘要

In this paper, we study the homogenization of 3D non-homogeneous incompressible Navier–Stokes system in perforated domains with holes of critical size. Under very mild assumptions concerning the shape of the obstacles and their mutual distance, we show that when \(\varepsilon \rightarrow 0\) ε → 0 , the velocity and density converge to a solution of the non-homogeneous incompressible Navier–Stokes system with a friction term of Brinkman type.