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<p>Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In Elgindi and Huang (Elgindi, Tarek M., and Yupei Huang. "Regular and Singular Steady States of the 2D Incompressible Euler Equations near the Bahouri–Chemin Patch." Arch.Ration.Mech.Anal.249(1),1-31(2025) ),a family of singular steady states near the Bahouri–Chemin patch was introduced. In this paper, we obtain the optimal convergence results for the singular steady states constructed in Elgindi and Huang (2025) to the Bahouri–Chemin patch. We first derive a boundary Harnack principle, and then obtain the optimal convergence results using the singular integral representation based on Green’s function.</p>

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Optimal Hölder convergence of a class of singular steady states to the Bahouri–Chemin patch

  • 期刊论文

  • 发表日期：

    2025年6月28日

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  • Yupei Huang,
  • Chilin Zhang

摘要

Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In Elgindi and Huang (Elgindi, Tarek M., and Yupei Huang. "Regular and Singular Steady States of the 2D Incompressible Euler Equations near the Bahouri–Chemin Patch." Arch.Ration.Mech.Anal.249(1),1-31(2025) ),a family of singular steady states near the Bahouri–Chemin patch was introduced. In this paper, we obtain the optimal convergence results for the singular steady states constructed in Elgindi and Huang (2025) to the Bahouri–Chemin patch. We first derive a boundary Harnack principle, and then obtain the optimal convergence results using the singular integral representation based on Green’s function.