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Non-unique vanishing-viscosity solutions of 2D Euler with vorticity in LpL^p

Primarily AI-generated textHuman understanding: no partsmath.AP — Analysis of PDEs

Contributed by Umberto Pappalettera, Massimo Sorella ↗

Version 1 / Oct 17, 2026 / CC BY 4.0

Abstract

For every finite p>2p>2, we construct one real compactly supported zero-circulation initial vorticity in L1(R2)∩Lp(R2)L^1(\mathbb R^2)\cap L^p(\mathbb R^2) whose unforced Navier--Stokes evolutions have two distinct strong vanishing-viscosity accumulation paths. Both limits are renormalized unforced Euler solutions with the same strong initial trace. The construction uses a fixed infinite concentric stack, a smooth unstable fourfold profile, actual positive scalar envelopes, and a finite nonlinear expansion retaining the interacting harmonic histories. Discounted source history is controlled through the complete prospective receiver stop, and exact-cap normalization yields a depth-uniform outgoing reset. Protected first crossings, phase degree and a sparse phase assignment then separate the two limits. The analytical preliminaries, finite-sector spectral scope, source-reference comparison and uniform parameter order are included in the proof.

Provenance statement

The manuscript was developed autonomously by ChatGPT 6.1 Sol and the manuscript is fully AI generated. The contributors did not edit the resulting PDF and do not claim authorship of the manuscript’s text or proofs. We are sharing the manuscript here because we would like the mathematics behind this result to be prioritized over a counterproductive race to upload AI-generated proofs to arXiv. We are organizing a reading group to study the claimed proof in detail, identify and deeply understand its main underlying ideas, and communicate them in a form more accessible to the mathematical community, for instance as a set of lecture notes. We encourage anyone interested in studying the manuscript to get in touch with us. More details for source material can be found at the webpage: https://2deuler.github.io/2deuler/

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References

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Version history

  1. v1Submitted by Massimo SorellaInitial depositCurrentOct 17, 2026