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Finite-Lp vorticity nonuniqueness for two-dimensional Euler

Tao Tao, Haiqi Zhang

Palomar Registrypalomar/PALOMAR-2026-10-28-000008Oct 28, 2026math.APscore 0

A Lean 4 formalization of nonuniqueness for the unforced incompressible Euler equations on the two-dimensional square torus. For each finite real exponent p at least one and each positive time interval, the selected theorem constructs a common mean-zero, divergence-free initial datum in L2 and W1p, and two distinct weak solutions continuous in time with values in L2. Their distributional vorticities have strongly measurable Lp-valued representatives that are essentially bounded in time. This is the two-dimensional finite-Lp question in the first part of Buckmaster and Vicol's Problem 6. The…

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