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<p>In this paper, we study the convergence of the solutions to the Dirichlet problem of the incompressible micropolar fluid equations with full anisotropic dissipation toward the solution to the ideal micropolar fluid equations in the upper half-plane. By choosing suitable correctors, we find that if the vertical dissipation of horizontal fluid velocity, the vertical angular viscosity and the micro-rotation viscosity vanish more quickly than the others, the vanishing dissipation limit exists in <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi mathvariant="normal">∞</mi> </msup> <mo stretchy="false">(</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mi>T</mi> <mo stretchy="false">]</mo> <mo>;</mo> <msup> <mi>L</mi> <mn>2</mn> </msup> <mo stretchy="false">(</mo> <msubsup> <mi mathvariant="double-struck">R</mi> <mo>+</mo> <mn>2</mn> </msubsup> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$L^{\infty }([0,T];L^{2}(\mathbb{R}^{2}_{+}))$</EquationSource> </InlineEquation>. In addition, we deal with the difficulty caused by the micro-rotation viscosity. Further, we obtain the convergence rate.</p>

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Vanishing Dissipation Limit for the 2D Anisotropic Micropolar Fluid Equations in the Half-Plane

  • 期刊论文

  • 发表日期：

    2026年2月2日

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  • Xiaoxue Kai,
  • Qian Li,
  • Xiaojing Xu

摘要

In this paper, we study the convergence of the solutions to the Dirichlet problem of the incompressible micropolar fluid equations with full anisotropic dissipation toward the solution to the ideal micropolar fluid equations in the upper half-plane. By choosing suitable correctors, we find that if the vertical dissipation of horizontal fluid velocity, the vertical angular viscosity and the micro-rotation viscosity vanish more quickly than the others, the vanishing dissipation limit exists in L ∞ ( [ 0 , T ] ; L 2 ( R + 2 ) ) $L^{\infty }([0,T];L^{2}(\mathbb{R}^{2}_{+}))$ . In addition, we deal with the difficulty caused by the micro-rotation viscosity. Further, we obtain the convergence rate.