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<p>We consider the Cauchy problem for chemotaxis-Navier-Stokes equations with nonlinear diffusion <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Δ</mi> <msup> <mi>n</mi> <mi>m</mi> </msup> </math></EquationSource> <EquationSource Format="TEX">$\Delta n^{m}$</EquationSource> </InlineEquation> in <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="double-struck">R</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$\mathbb{R}^{2}$</EquationSource> </InlineEquation>. By exploring the new a priori estimates, we establish the global existence of weak solutions to the chemotaxis-Navier-Stokes equations with <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <mi>m</mi> <mo>&gt;</mo> <mn>1</mn> </math></EquationSource> <EquationSource Format="TEX">$m&gt;1$</EquationSource> </InlineEquation>. This result extends the bounded domain in reference (Tao and Winkler in Discrete Contin. Dyn. Syst. 32:1901–1914, <CitationRef CitationID="CR18">2012</CitationRef>) to the entire space.</p>

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Global Existence of Weak Solution for the 2D Chemotaxis-Navier-Stokes Equations with Arbitrary Porous Medium Diffusion

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Mingxi Li,
  • Qian Zhang

摘要

We consider the Cauchy problem for chemotaxis-Navier-Stokes equations with nonlinear diffusion Δ n m $\Delta n^{m}$ in R 2 $\mathbb{R}^{2}$ . By exploring the new a priori estimates, we establish the global existence of weak solutions to the chemotaxis-Navier-Stokes equations with m > 1 $m>1$ . This result extends the bounded domain in reference (Tao and Winkler in Discrete Contin. Dyn. Syst. 32:1901–1914, 2012) to the entire space.