Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 495, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2020.124695
Keywords
Euler equations; Rotating vortex patch; Radial symmetry; V-state
Categories
Funding
- China Postdoctoral Science Foundation [2019M661261]
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This note discusses the radial symmetry property of rotating vortex patches for the 2D incompressible Euler equations in the unit disk. It shows that under certain conditions, a rotating vortex patch must be a disk.
In this note, we consider the radial symmetry property of rotating vortex patches for the 2D incompressible Euler equations in the unit disk. By choosing a suitable vector field to deform the patch, we show that each simply-connected rotating vortex patch D with angular velocity Omega, Omega >= max{1/2, (2l(2))/(1 - l(2))(2)} or Omega <= -(2l(2))/(1 - l(2))(2), where l = sup(x is an element of D) vertical bar x vertical bar, must be a disk. The main idea of the proof, which has a variational flavor, comes from a recent paper of Gomez-Serrano-Park-Shi-Yao, arXiv :1908 .01722, where radial symmetry of rotating vortex patches in the whole plane was studied. (C) 2020 Elsevier Inc. All rights reserved.
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