Preprint · Zenodo · October 18, 2026

Linear stability of asymmetric Burgers vortices at large circulation beyond the half-strain threshold

Abstract

The asymmetric Burgers vortex is a steady vortex sustained by a non-axisymmetric linear strain with asymmetry ratio λ ∈ [0,1). At large circulation α it exists and is locally unique for every λ < 1 (Maekawa), but its linear stability was known only for λ < 1/2. We prove that for every λ ≤ 0.9399 and every sufficiently large α, Maekawa's vortex is linearly stable: the linearized operator satisfies Re⟨A*w, w⟩ ≤ −(k_λ − δ)‖w‖² on zero-mass perturbations in an explicit weighted space, with an explicit rate k_λ > 0 (for example k_0.5 ≥ 0.240, k_0.9 ≥ 0.0222). The proof uses the vortex's own weight 1/ω*, in which every term of size α except one is exactly neutral; an exact identity expressing the Fisher information of the vortex relative to the Gaussian through its second moments; an asymptotic for the next-order quadrupole proved by duality; rotation-adapted barriers giving two-sided Gaussian tails and closeness to the Gaussian on a logarithmic zone, uniformly in α; and a computer-assisted (interval arithmetic, Arb) proof that the α → ∞ limiting quadratic form is coercive. The record contains the paper, its LaTeX source, and the interval-arithmetic certificates with their outputs (burgers_certificates.zip; Python 3 + python-flint; see README inside). The work was carried out with substantial help from generative AI (Anthropic's Claude), as disclosed in the paper's acknowledgements.

Fluid Dynamics and Turbulent FlowsNavier-Stokes equation solutionsAdvanced Mathematical Physics Problemslinear stabilityweighted function spacesFisher information

Linear stability of asymmetric Burgers vortices at large circulation beyond the half-strain threshold

Abstract

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