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<p>Lately, Chen et al. (J. Dynam. Differential Equations 36:3311-3361, 2024) established the global well-posedness and the optimal time decay rates of strong solutions to the compressible Oldroyd-B model in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2531_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^2(\mathbb {R}^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-framework. In this paper, we further show the optimal time decay rates of the highest spatial derivative of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2531_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {T}-k\eta \mathbb {I}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="double-struck">T</mi> <mo>-</mo> <mi>k</mi> <mi>η</mi> <mi mathvariant="double-struck">I</mi> </mrow> </math></EquationSource> </InlineEquation>. This work can be seen as a refinement of previous related results.</p>

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Optimal decay rates of the compressible Oldroyd-B model in \(\mathbb {R}^2\)

  • 期刊论文

  • 发表日期：

    2025年6月25日

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  • Sili Liu,
  • Boling Guo

摘要

Lately, Chen et al. (J. Dynam. Differential Equations 36:3311-3361, 2024) established the global well-posedness and the optimal time decay rates of strong solutions to the compressible Oldroyd-B model in \(H^2(\mathbb {R}^2)\) H 2 ( R 2 ) -framework. In this paper, we further show the optimal time decay rates of the highest spatial derivative of \(\mathbb {T}-k\eta \mathbb {I}\) T - k η I . This work can be seen as a refinement of previous related results.