Generic small-scale creation in the two-dimensional Euler equation
Analysis of PDEs
2026-03-16 v1
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 set of initial data, the solutions lose regularity in infinite time, thereby confirming a long-standing conjecture of Yudovich in the smooth setting.
Cite
@article{arxiv.2603.13079,
title = {Generic small-scale creation in the two-dimensional Euler equation},
author = {Thomas Alazard and Ayman Rimah Said},
journal= {arXiv preprint arXiv:2603.13079},
year = {2026}
}