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<p>We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an “algebra tool kit” to deal with limit and jump relations of layer operators. We do that first on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> for operators acting on a distribution supported on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\{x_{n} = 0\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>=</mo> <mn>0</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation> and then in general on (possibly non-compact) manifolds. We use these results to study the limit and jump relations of the layer potential operators associated to our generalized Stokes operators. As an application, we obtain well-posedness results for the Stokes system.</p>

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Well-Posedness of a Generalized Stokes Operator on Smooth Bounded Domains via Layer-Potentials

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月21日

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  • Mirela Kohr,
  • Victor Nistor,
  • Wolfgang L. Wendland

摘要

We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an “algebra tool kit” to deal with limit and jump relations of layer operators. We do that first on \(\mathbb {R}^{n}\) R n for operators acting on a distribution supported on \(\{x_{n} = 0\}\) { x n = 0 } and then in general on (possibly non-compact) manifolds. We use these results to study the limit and jump relations of the layer potential operators associated to our generalized Stokes operators. As an application, we obtain well-posedness results for the Stokes system.