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<p>We study a stationary generalized Boussinesq system in 3D bounded domains with homogeneous Dirichlet boundary conditions. We prove the existence of weak solutions applying the Leray–Schauder fixed-point principle and an iteration technique in suitably <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-norms. In particular, we consider the case where the thermal diffusion <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\kappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> is a non-negative function.</p>

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Existence of weak solutions for a generalized Boussinesq model in steady-state

  • 期刊论文

  • 发表日期：

    2025年12月29日

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  • Cristian Duarte-Leiva,
  • Sebastián Lorca,
  • Exequiel Mallea-Zepeda

摘要

We study a stationary generalized Boussinesq system in 3D bounded domains with homogeneous Dirichlet boundary conditions. We prove the existence of weak solutions applying the Leray–Schauder fixed-point principle and an iteration technique in suitably \(L^p\) L p -norms. In particular, we consider the case where the thermal diffusion \(\kappa \) κ is a non-negative function.