Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity

Hyungjun Choi

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arXiv · 2610.37653

Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity

Hyungjun Choi

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Abstract

We construct two distinct solutions of the two-dimensional incompressible Euler equation with the same initial vorticity in $\bigcap_{1\le p<\infty}L^p(\mathbb R^2)$. The vorticities are compactly supported in space and have mean zero, so the corresponding velocities have finite energy. The nonuniqueness mechanism is a cascade of transitions in quadrupole dynamics across infinitely many scales.

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Hyungjun Choi. 2026-10-27. Nonuniqueness of Solutions to 2D Incompressible Euler Equations with Unbounded Vorticity. https://arxiv.org/abs/2610.37653

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