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<p>We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_3075_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(U^2\)</EquationSource> </InlineEquation>-type spaces to prove the small data global well-posedness in the critical Besov space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="526_2025_3075_Article_IEq2.gif" Format="GIF" Height="28" Rendition="HTML" Resolution="72" Type="Linedraw" Width="207" /> </InlineMediaObject> <EquationSource Format="TEX">\(\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb {R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb {R}^n)\ (n\ge 2)\)</EquationSource> </InlineEquation>.</p>

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Global well-posedness for incompressible Hookean elastodynamics in the critical Besov spaces

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Zexian Zhang,
  • Yi Zhou

摘要

We identify the wave maps type nonlinearities of incompressible Hookean elastodynamics equations in Lagerangian coordinates, and iterate them in the adapted \(U^2\) -type spaces to prove the small data global well-posedness in the critical Besov space \(\dot{B}^{\frac{n}{2}+1}_{2,1}(\mathbb {R}^n)\times \dot{B}^{\frac{n}{2}}_{2,1}(\mathbb {R}^n)\ (n\ge 2)\) .