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<p>In this paper, we are concerned with the Cauchy problem for the chemotaxis-Navier-Stokes equations in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="30_2025_1081_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. By making use of the Fourier localization and a high-low decomposition, we prove the optimal time decay rates of solutions in critical Besov spaces.</p>

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Optimal decay rates for the 3D chemotaxis-Navier-Stokes equations in critical Besov spaces

  • 期刊论文

  • 发表日期：

    2025年6月2日

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  • Qian Zhang

摘要

In this paper, we are concerned with the Cauchy problem for the chemotaxis-Navier-Stokes equations in \(\mathbb {R}^{3}\) R 3 . By making use of the Fourier localization and a high-low decomposition, we prove the optimal time decay rates of solutions in critical Besov spaces.