Year: 2026
Type: article
Abstract: 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 $C^0_t (W^{\frac{1}{3},-3} \cap L^{\infty-})$. More precisely, for every $\beta\lt \frac{1}{3}$, we can construct such solutions in the space $C^0_t (B^\beta_{3,\infty} \cap L^{\frac{1}{1-3\beta}})$.
Source: Annals of Mathematics
Authors: Vikram Giri, Hyunju Kwon, Matthew Novack
Institutions: University of Zurich, ETH Zurich, Purdue University West Lafayette
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4378942455