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<p>For the evolutionary Stokes problem with dynamic boundary conditions, we show the maximal regularity of weak solutions in time. Due to the characterization of <i>R</i>-sectorial operators on Hilbert spaces, the proof reduces to identifying the appropriate functional analytic setting and proving that the corresponding operator is sectorial, i.e., that it generates an analytic semigroup.</p>

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Maximal Regularity of Stokes Problem with Dynamic Boundary Condition — Hilbert Setting

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月30日

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  • Tomáš Bárta,
  • Paige Davis,
  • Petr Kaplický

摘要

For the evolutionary Stokes problem with dynamic boundary conditions, we show the maximal regularity of weak solutions in time. Due to the characterization of R-sectorial operators on Hilbert spaces, the proof reduces to identifying the appropriate functional analytic setting and proving that the corresponding operator is sectorial, i.e., that it generates an analytic semigroup.