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<p>A result of Gevrey regularity is ascertained for a semigroup which models a fluid–structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2625_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {O}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">O</mi> </math></EquationSource> </InlineEquation>. On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the conclusion of Gevrey regularity is an appropriate estimation of the resolvent of the associated <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2625_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(C_0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>C</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-semigroup operator. Moreover, a numerical scheme and example is provided which empirically demonstrates smoothing of the fluid–structure semigroup.</p>

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Gevrey Regularity for A Fluid–Structure Interaction Model

  • 期刊论文

  • 发表日期：

    2025年2月17日

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  • George Avalos,
  • Dylan McKnight,
  • Sara McKnight

摘要

A result of Gevrey regularity is ascertained for a semigroup which models a fluid–structure interaction problem. In this model, the fluid evolves in a piecewise smooth or convex geometry \(\mathcal {O}\) O . On a portion of the boundary, a fourth order plate equation is coupled with the fluid through pressure and matching velocities. The key to obtaining the conclusion of Gevrey regularity is an appropriate estimation of the resolvent of the associated \(C_0\) C 0 -semigroup operator. Moreover, a numerical scheme and example is provided which empirically demonstrates smoothing of the fluid–structure semigroup.