Time-periodic non-radial solutions near monotone vortices in linearized 2D Euler

2025/12/01 by Castro, Ángel, Daniel Lear, Lear, Daniel
Engineering · Mathematics · #35Q31 #35Q35 #76B03 #76E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.01730

openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

We study the linearized 2D Euler equations around radial vortex profiles. Previous works have shown that the strict monotonicity of the vorticity profile leads to axisymmetrization and inviscid damping of non-radial perturbations. Given any strictly decreasing radial vortex, we construct arbitrarily close (in low Hölder norms C^α, with 0<α< 1) radial profiles that are merely non-increasing, for which non-radial, time-periodic solutions to the linearized equation exist. This shows that both axisymmetrization and inviscid damping are not robust under small, low-regularity perturbations of the background profile that violate strict monotonicity.

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Related

• Time periodic solutions close to localized radial monotone profiles for the 2D Euler equations
• Stability of radially symmetric, monotone vorticities of 2D Euler equations
• Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations
• Mathematical Analysis of Axisymmetrization and Enhanced Inviscid Damping in 2D Linearized Euler Flow
• Axi-symmetrization near point vortex solutions for the 2D Euler equation