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<p>This paper is concerned with a double chemotaxis Navier-Stokes system in the whole space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_836_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {R}}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_836_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(N\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>. We prove new results concerning the existence of global in time solutions, self-similarity and asymptotic behaviour in a framework of critical Besov-weak-Herz spaces. A central role in the proof of the main results is the derivation and careful use of a set of new product estimates in the context of Besov-weak-Herz spaces.</p>

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Application of Besov-weak-Herz spaces to the theoretical study of a double chemotaxis-fluid model

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Jhean E. Pérez-López,
  • Diego A. Rueda-Gómez,
  • Sergio A. Jiménez-Jerez

摘要

This paper is concerned with a double chemotaxis Navier-Stokes system in the whole space \({\mathbb {R}}^N\) R N for \(N\ge 2\) N ≥ 2 . We prove new results concerning the existence of global in time solutions, self-similarity and asymptotic behaviour in a framework of critical Besov-weak-Herz spaces. A central role in the proof of the main results is the derivation and careful use of a set of new product estimates in the context of Besov-weak-Herz spaces.