Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane

Shaoqing Chen; Yongzhong Sun

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arXiv · 2605.31541

Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane

Shaoqing Chen·Yongzhong Sun

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Abstract

It has been conjectured that generic smooth solutions of the two-dimensional Euler equation exhibit linear growth of vorticity gradients. We prove an elementary arbitrary-background perturbation principle in the odd symmetric setting. More precisely, for any compactly supported nonnegative function in the half-plane, one can find an arbitrarily small smooth nonnegative perturbation whose associated solution undergoes linear-in-time filamentation in the quadrant. The main ingredients are the lower bound of the center of mass given by Iftimie-Sideris-Gamblin, and the velocity estimate for the sparse part to capture those slowly moving particles.

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Shaoqing Chen, Yongzhong Sun. 2026-05-29. Remarks on Linear Growth of Vorticity Gradients and Support Diameters for 2D Euler Flow in Half-Plane. https://arxiv.org/abs/2605.31541

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