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<p>We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(W^{1,p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>W</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>p</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(W^{2,p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>W</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>p</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(1&lt;p&lt;\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>&lt;</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation> for the velocity field) in bounded domains of minimal regularity. Interestingly, exactly one derivative more is required for the local boundary charts compared to the case of no-slip boundary conditions. We demonstrate the sharpness of our results by a propos examples.</p>

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The Stokes problem with Navier boundary conditions in irregular domains

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月18日

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  • Dominic Breit,
  • Sebastian Schwarzacher

摘要

We consider the steady Stokes equations supplemented with Navier boundary conditions including a non-negative friction coefficient. We prove maximal regularity estimates (including the prominent spaces \(W^{1,p}\) W 1 , p and \(W^{2,p}\) W 2 , p for \(1<p<\infty \) 1 < p < ∞ for the velocity field) in bounded domains of minimal regularity. Interestingly, exactly one derivative more is required for the local boundary charts compared to the case of no-slip boundary conditions. We demonstrate the sharpness of our results by a propos examples.