The L3-based strong Onsager theorem

• 成果类型: Article
• 署名作者: Giri, Vikram; Kwon, Hyunju; Novack, Matthew
• 署名单位: University of Zurich; Swiss Federal Institutes of Technology Domain; ETH Zurich; Purdue University System; Purdue University
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2026.204.1.4
• 发表日期: 2026-07
• 页码: 265-421
• 关键词: strong Onsager conjecture; local energy inequality; WEAK SOLUTIONS; incompressible euler; energy-conservation; DISSIPATION; EQUATIONS; conjecture; fluid

摘要

In this work, we prove the L-3-based strong Onsager conjecture for the three-dimensional Euler equations. Our main theorem states that there exist weak solutions which dissipate the total kinetic energy, satisfy the local energy inequality, and belong to C-t(0)(W-1/3-,W-3 boolean AND L infinity-). More precisely, for every beta < 1/3, we can construct such solutions in the space C-t(0)(B-3,infinity(beta) boolean AND 1/L1-3 beta).