This proof demonstrates orbital stability in Euler flows, indicating that greater radial symmetry may reduce stability.
We provide a short proof of the ‐orbital stability of a class of explicit steady Euler flows in a disk by establishing a quantitative estimate. The main idea is to exploit the conserved quantities of the Euler equation, including the kinetic energy, the enstrophy, and the moment of impulse. Our result seems to suggest that the stronger radial symmetry leads to weaker stability.
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Wang et al. (2026) studied this question.
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