Regular and Singular Steady States of 2D incompressible Euler equations near the Bahouri-Chemin Patch

2022/07/26 by Tarek M. Elgindi, Elgindi, Tarek M., Yupei Huang +1 · 2 citations
Earth and Planetary Sciences · Mathematics · #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2207.12640

openalex publication_date 2022/07/26 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

We consider steady states of the two-dimensional incompressible Euler equations in \mathbbT² and construct smooth and singular steady states around a particular singular steady state. More precisely, we construct families of smooth and singular steady solutions that converge to the Bahouri-Chemin patch.

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• Desingularization of nondegenerate rotating vortex patches
• Homogeneous steady states for the generalized surface quasi-geostrophic equations

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