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<p>This paper focuses on the hydrodynamic limit problem from a kinetic Cucker–Smale model with a confining potential toward the self-organized hydrodynamic system. This paper aims to establish a uniform-in-<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation> convergence rate for the asymptotic expansion ansatz, and hence significantly improves the result obtained in Jiang–Luo–Zhang (Math Models Methods Appl Sci 34:2395–2467, 2024). The key ingredient of the proof is to consider a new decomposition for the remainder function, by handling the contribution of the macroscopic density separately. Moreover, the convergence holds valid in any higher-order Sobolev spaces with the general regularity index.</p>

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On the Hydrodynamic Limits of Kinetic Cucker–Smale Model

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Ning Jiang,
  • Hongtao Xu,
  • Teng-Fei Zhang

摘要

This paper focuses on the hydrodynamic limit problem from a kinetic Cucker–Smale model with a confining potential toward the self-organized hydrodynamic system. This paper aims to establish a uniform-in- \(\varepsilon \) ε convergence rate for the asymptotic expansion ansatz, and hence significantly improves the result obtained in Jiang–Luo–Zhang (Math Models Methods Appl Sci 34:2395–2467, 2024). The key ingredient of the proof is to consider a new decomposition for the remainder function, by handling the contribution of the macroscopic density separately. Moreover, the convergence holds valid in any higher-order Sobolev spaces with the general regularity index.