On the rigidity of uniformly rotating vortex patch near the Rankine vortex

In this paper, we study the uniformly rotating vortex patch solutions for the 2D incompressible Euler equations. Specifically, we prove that if the patch solution is close to the Rankine vortex in a certain weak topology, it is either the Kirchhoff ellipses or the Rankine vortex.

Saved in:
Bibliographic Details
Main Author Huang, Yupei
Format Journal Article
LanguageEnglish
Published 19.12.2023
Subjects
Mathematics - Analysis of PDEs
Online AccessGet full text

Cover

More Information
Summary:In this paper, we study the uniformly rotating vortex patch solutions for the 2D incompressible Euler equations. Specifically, we prove that if the patch solution is close to the Rankine vortex in a certain weak topology, it is either the Kirchhoff ellipses or the Rankine vortex.
DOI:10.48550/arxiv.2312.12711