We construct two distinct solutions of the two-dimensional incompressible Euler equation with the same initial vorticity in 1≤ p<∞Lᵖ( R²). 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) studied this question.
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