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arXiv · 2603.13079

Generic small-scale creation in the two-dimensional Euler equation

Thomas Alazard·Ayman Rimah Said
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Abstract

The Cauchy problem for the two-dimensional incompressible Euler equation is globally well-posed for smooth initial data. In this paper, we show that for a dense $G_\delta$ set of initial data, the solutions lose regularity in infinite time, thereby confirming a long-standing conjecture of Yudovich in the smooth setting.

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Thomas Alazard, Ayman Rimah Said. 2026-03-13. Generic small-scale creation in the two-dimensional Euler equation. https://arxiv.org/abs/2603.13079

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