Year: 2026
Type: preprint
Abstract: In this paper, we prove the existence of an extensive class of initial data--characterized by intermittency dimension and roughness--for which the d-dimensional Euler equations (d \ge 2) admit a decreasing energy channel with infinitely many admissible solutions arising from the same initial data. This class includes initial data in C^{1-κ}(\mathbb{T}^d) and W^{1,p}(\mathbb{T}^d) for any 0 < κ< 1 and 2 < p < \infty, thereby demonstrating the sharpness of the Lions and Yudovich uniqueness principles. Our proof is based on a new backward convex integration scheme employing approximate Λ-Euler equations to reduce the initial error and on uncovering a quantitative relationship between regularity, energy, and intermittency.
Source: arXiv (Cornell University)
Authors: Cheskidov, Alexey, Zeng, Zirong, Zhang, Deng
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222930856