Quantitative stability of a class of explicit steady Euler flows in a disk

2025/10/16 by Wang, Fatao, Wang, Guodong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.14394

Abstract

We provide a short proof of the L²-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 fluid impulse. Our result seems to suggest that more radial symmetry leads to stronger instability.

Citations

• Quantitative stability of the Rossby--Haurwitz waves of degree two for the Euler equation on \mathbbS²
• Stability of a class of exact solutions of the incompressible Euler equation in a disk
• Remark on the Stability of Energy Maximizers for the 2D Euler equation on \mathbbT²
• Stability of degree-2 Rossby-Haurwitz waves
• Nonlinear stability of sinusoidal Euler flows on a flat two-torus

Related

• Stability of a class of exact solutions of the incompressible Euler equation in a disk
• On the positive constant in Arnold's second stability theorem for a bounded domain
• Nonlinear stability of planar steady Euler flows associated with semistable solutions of elliptic problems
• Characterization of steady solutions to the 2D Euler equation
• Stability analysis of two-dimensional ideal flows with applications to viscous fluids and plasmas