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<p>In this paper, we investigate the Cauchy problem for the <i>d</i>-dimensional incompressible chemotaxis-Navier–Stokes equations of consumption type with logistic source in the partially or fully inviscid case. By exploring some new modified energy estimates, we firstly establish the local well-posedness of the system in Sobolev spaces for partially (fully) inviscid case with nonvanishing initial data. Next, in a new function space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2453_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="37" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {X}^{m, \gamma }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">X</mi> </mrow> <mrow> <mi>m</mi> <mo>,</mo> <mi>γ</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> proposed by Jeong–Kang [Commun. Math. Phys. 390 1175–1217, 2022], we show the local well-posedness result with vanishing initial data in the fully inviscid case.</p>

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Well-posedness for the chemotaxis-Navier–Stokes system of consumption type with logistic source

  • 期刊论文

  • 发表日期：

    2025年2月26日

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  • Qunyi Bie,
  • Hui Fang

摘要

In this paper, we investigate the Cauchy problem for the d-dimensional incompressible chemotaxis-Navier–Stokes equations of consumption type with logistic source in the partially or fully inviscid case. By exploring some new modified energy estimates, we firstly establish the local well-posedness of the system in Sobolev spaces for partially (fully) inviscid case with nonvanishing initial data. Next, in a new function space \(\mathcal {X}^{m, \gamma }\) X m , γ proposed by Jeong–Kang [Commun. Math. Phys. 390 1175–1217, 2022], we show the local well-posedness result with vanishing initial data in the fully inviscid case.