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arXiv · 2311.11112

Optimal H{\"o}lder convergence of a class of singular steady states to the Bahouri-Chemin patch

Yupei Huang·Chilin Zhang
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Abstract

Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In \cite{elgindi2022regular}, 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 \cite{elgindi2022regular} 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.

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Yupei Huang, Chilin Zhang. 2023-11-18. Optimal H{\"o}lder convergence of a class of singular steady states to the Bahouri-Chemin patch. https://doi.org/10.1007/s00526-025-03048-9

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