Scholarlink

<p>This paper is concerned with the analysis of mixed Dirichlet–Robin boundary value problems for the anisotropic Brinkman and Darcy–Forchheimer–Brinkman systems, as well as a system of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d \ge 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> coupled anisotropic Darcy–Forchheimer–Brinkman equations in bounded Lipschitz domains in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}^n, n = 2,3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. These systems provide general models for flows of anisotropic viscous incompressible fluids in heterogeneous and multidisperse porous media. By combining a variational approach and fixed-point techniques, we establish the existence and uniqueness of weak solutions in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{L}^2-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mtext>L</mtext> <mn>2</mn> </msup> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>based Sobolev spaces under suitable smallness conditions on the given data. To demonstrate the applicability of the theoretical results, we carry out a numerical investigation of the lid-driven flow problem in a square monodisperse or bidisperse porous cavity containing a solid circular obstacle, employing a Robin boundary condition on the moving lid and examining the effect of key physical parameters on the flow behavior.</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

Mixed Dirichlet–Robin problem for coupled anisotropic Navier–Stokes-type systems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月15日

查看全文
  • Andrei Gasparovici

摘要

This paper is concerned with the analysis of mixed Dirichlet–Robin boundary value problems for the anisotropic Brinkman and Darcy–Forchheimer–Brinkman systems, as well as a system of \(d \ge 1\) d ≥ 1 coupled anisotropic Darcy–Forchheimer–Brinkman equations in bounded Lipschitz domains in \(\mathbb {R}^n, n = 2,3\) R n , n = 2 , 3 . These systems provide general models for flows of anisotropic viscous incompressible fluids in heterogeneous and multidisperse porous media. By combining a variational approach and fixed-point techniques, we establish the existence and uniqueness of weak solutions in \(\textrm{L}^2-\) L 2 - based Sobolev spaces under suitable smallness conditions on the given data. To demonstrate the applicability of the theoretical results, we carry out a numerical investigation of the lid-driven flow problem in a square monodisperse or bidisperse porous cavity containing a solid circular obstacle, employing a Robin boundary condition on the moving lid and examining the effect of key physical parameters on the flow behavior.