Optimal H\"older convergence of a class of singular steady states to the Bahouri-Chemin patch
Abstract
Singular steady states are important objects in obtaining ill-posedness results for 2D incompressible Euler equations. In 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 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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